Multiobjective quadratic optimization. Medical search. Frequent questions

ANTIGONE - a deterministic global optimization MINLP solver. (wikipedia.org)
Global optimization with add-on toolbox. (wikipedia.org)
Global optimization. (warwick.ac.uk)
Understand global optimization methods. (warwick.ac.uk)
You can also use the 'free' BMIBNB branch and bound global optimization solver under YALMIP, but you will generally need to have available a local nonlinear solver for ti to call,such as FMINCON or IPOPT (under OPTI-toolbox) and a MILP solver for it to call. (stackexchange.com)
In addition, the "EzOptimizer" includes a method, which is referred to a "hybrid optimization method", for combining local and global optimization algorithms such that their drawbacks can be overcome, thus permitting the use of the salient features of the two algorithms. (snu.ac.kr)
R. Paulavičius, J. Žilinskas (2014) Simplicial Global Optimization . (mii.lt)
2016) Advances in Stochastic and Deterministic Global Optimization . (mii.lt)
2007) Models and Algorithms for Global Optimization . (mii.lt)

HEEDS MDO - multidisciplinary design optimization using SHERPA, a hybrid, adaptive optimization algorithm. (wikipedia.org)
Instead of guessing and or trial and error method, genetic algorithm (GA)-based optimization algorithm is implemented to tune PID parameters and FLC membership functions' range and scaling factors. (springeropen.com)
Kesarkar and Selvaganesan ( 2015 ) designed fractional order PID controller using artificial bee colony algorithm with objective functions such as integral absolute error, integral square error, and integral time absolute error implemented to a multi-modal complex optimization problem. (springeropen.com)
and MIDACO - a great evolutionary processing algorithm pertaining to multi-objective, continuous and integer optimization. (pepishairdresser.com)
We propose M Q A P V I Z, a divide-and-conquer multi-objective optimization algorithm to compute large-scale data visualizations. (edu.au)
The algorithm was first introduced in the case of two disciplines (m = 1, M = 2), and successfully applied to optimum shape design optimization in compressible aerodynamics concurrently with a secondary discipline [5] [9]. (hal.science)
Aiming to the special real-integer hybrid variables optimization problems, the non-dominated sorting genetic algorithm II (NSGA-II) is employed and improved. (extrica.com)
The influences of algorithm parameters on the optimization procedure are also investigated. (extrica.com)
Zheng and Cai [10] employed four different nonlinear optimization methods/algorithms (sub-problem approximation method, the first-order method, sequential quadratic programming (SQP) and genetic algorithm (GA)) to find the optimal locations and lengths of the CLD patches, to minimize displacement amplitude at the middle beam. (extrica.com)
Al-Ajmi and Bourisli [11] optimized CLD segments' length using the genetic algorithm (GA). The optimization procedure was only able to identify a distribution of segments for a single mode. (extrica.com)
The "EzOptimizer", which is written in C++ language, includes a number of optimization algorithms, such as the method of feasible directions (MFD), sequential quadratic programming (SQP), sequential linear programming (SLP), genetic algorithm (GA), multi-objective programming, linear programming, etc. (snu.ac.kr)
For instance , if an search engine optimization algorithm would be to model a motor by simply creating and running simulations of different fixed-point versions of the identical system, it would search for products that generate the best outcome based on the specified behavioral constraints. (karenabrego.com)
and MIDACO - a great evolutionary calculating algorithm intended for multi-objective, constant and integer optimization. (karenabrego.com)
Dai Y-h, and Schittkowski K (2008) A sequential quadratic programming algorithm with non-monotone line search, Pacific Journal of Optimization, 4:335-351. (pyopt.org)
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. (pyopt.org)
Frick, JD, (1989) Variable-Metric Algorithm For Constrained Optimization. (pyopt.org)
Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: Harmony search. (pyopt.org)
Gill PE, Murray W, Saunders MA (2002) SNOPT: An SQP algorithm for large-scale constrained optimization. (pyopt.org)
Schittkowski k (2011) A robust implementation of a sequential quadratic programming algorithm with successive error restoration. (pyopt.org)
In this paper, a hybrid optimization method, GA-SQP, is described in which the genetic algorithm (GA) is a stochastic method is combined with the sequential quadratic programming (SQP) method, which is a deterministic method. (uaeu.ac.ae)
The power system stabilizers (PSSs) parameters tuning problem is converted to an optimization problem which is solved by hybrid GA- SQP optimization algorithm. (uaeu.ac.ae)

A software package for sequential quadratic programming. (sbc.org.br)
Lawrence CT, Tits AL (1996) Nonlinear equality constraints in feasible sequential quadratic programming. (pyopt.org)
Liuzzi G, Lucidi S, Sciandrone M (2010) Sequential Penalty Derivative-free Methods for Nonlinear Constrained Optimization. (pyopt.org)

COPT Cardinal Optimizer - a mathematical high-performance optimization solver for large-scale problems including LP, MIP, SDP, (MI)SOCP, convex (MI)QP and convex (MI)QCP CPLEX - solver for linear and quadratic programming with continuous or integer variables (MIP). (wikipedia.org)
FICO Xpress - solver for linear and quadratic programming with continuous or integer variables (MIP). (wikipedia.org)
Use Matlab or similar numerical software to solve optimization problems using numerical algorithms and builtin/add-on optimization solver. (warwick.ac.uk)
Apply a solver to the optimization problem to find an optimal solution: a set of optimization variable values that produce the optimal value of the objective function, if any, and meet the constraints, if any. (mathworks.com)
Kuntsevich A, Kappel F (1997) SolvOpt manual: The solver for local nonlinear optimization problems. (pyopt.org)

To introduce general algorithms for convex and non-convex optimization problems arising in various application areas such as financial portfolio optimization, energy system planning, and engineering design optimization, and their computational aspects using a numerical software tool such as Matlab. (warwick.ac.uk)
Module introduction with examples of several optimization problems in various application areas such as financial portfolio optimization, energy system planning, and engineering design optimization, and review of mathematical background materials (linear algebra, calculus-derivatives, etc. (warwick.ac.uk)
We plan to cover various applications such as financial portfolio optimization, energy system planning, and engineering design optimization, and several solution algorithms. (warwick.ac.uk)

The central part of the book is dedicated to MATLABs Optimization Toolbox, which implements state-of-the-art algorithms for solving multiobjective problems, non-linear minimization with boundary conditions and restrictions, minimax optimization, semi-infinitely constrained minimization and linear and quadratic programming. (oreilly.com)
PyMOSO: Python software for solving multi-objective simulation optimization (MOSO) problems and for creating, comparing, and testing MOSO algorithms. (purdue.edu)
Physics-inspired optimisation algorithms have been proposed for deriving optimal or sub-optimal solutions to QUBOs. (deepai.org)
Quantum and quantum-inspired optimisation algorithms have shown promising performance when applied to academic benchmarks as well as real-world problems. (deepai.org)
Quantum and quantum-inspired optimisation algorithms are designed to sol. (deepai.org)
Optimisation algorithms designed to work on quantum computers or other s. (deepai.org)
Apply numerical algorithms for unconstrained and constrained convex optimization problems. (warwick.ac.uk)
You can use the toolbox solvers to find optimal solutions to continuous and discrete problems, perform tradeoff analyses, and incorporate optimization methods into algorithms and applications. (mathworks.com)
Build optimization-based decision support and design tools, integrate with enterprise systems, and deploy optimization algorithms to embedded systems. (mathworks.com)
MATLAB has helped accelerate our R&D and deployment with its robust numerical algorithms, extensive visualization and analytics tools, reliable optimization routines, support for object-oriented programming, and ability to run in the cloud with our production Java applications. (mathworks.com)
Mean-semivariance portfolio optimization with multiobjective evolutionary algorithms and technical analysis rules. (sbc.org.br)
Carola's main research activities are in the analysis of black-box optimization algorithms, both by mathematical and by empirical means. (sigevo.org)
His research activities deal with the foundations, the design and the analysis of stochastic local search and evolutionary algorithms, with a particular interest in multi-objective optimization and landscape analysis. (sigevo.org)

APMonitor - modeling language and optimization suite for large-scale, nonlinear, mixed integer, differential and algebraic equations with interfaces to MATLAB, Python, and Julia. (wikipedia.org)
Get full access to MATLAB Optimization Techniques and 60K+ other titles, with a free 10-day trial of O'Reilly. (oreilly.com)
MATLAB Optimization Techniques introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. (oreilly.com)
It begins by introducing the MATLAB environment and the structure of MATLAB programming before moving on to the mathematics of optimization. (oreilly.com)
fot_quadprogmat: Solves a quadratic optimization problem (with input in Matlab format). (scilab.org)
A mathematical model of nonlinear quarter car is developed and simulated for control and optimization in Matlab/Simulink® environment. (springeropen.com)
Attach:apm_python.png Attach:apm_matlab.png The APMonitor server is designed for large-scale optimization and accesses solvers of constrained, unconstrained, continuous, and discrete problems. (apmonitor.com)

Introduction to a software for modelling and solving optimization problems. (warwick.ac.uk)

ASTOS - AeroSpace Trajectory Optimization Software for launcher, re-entry and generic aerospace problems. (wikipedia.org)
BARON - optimization of algebraic nonlinear and mixed-integer nonlinear problems. (wikipedia.org)
This toolbox consists of open-source solvers for a variety of optimization problems: CLP for linear optimization, CBC for integer linear optimization, IPOPT (with MUMPS) for nonlinear optimization, and BONMIN for integer nonlinear optimization. (scilab.org)
A fractional programming problem arises in many types of optimization problems such as portfolio selection, production, information theory, and numerous decision making problems in management science. (hindawi.com)
The central concept in optimization is known as the duality theory which asserts that, given a (primal) minimization problem, the infimum value of the primal problem cannot be smaller than the supermom value of the associated (dual) maximization problem and the optimal values of primal and dual problems are equal. (hindawi.com)
11 ] derived Fritz John and Karush-Kuhn Tucker necessary and sufficient optimality condition for a class of nondifferentiable convex multiobjective fractional programming problems and established some duality theorems. (hindawi.com)
Duality for various forms of mathematical problems involving square roots of positive semidefinite quadratic forms has been discussed by many authors [ 10 , 23 - 25 ]. (hindawi.com)
In recent years, there has been significant research interest in solving Quadratic Unconstrained Binary Optimisation (QUBO) problems. (deepai.org)
These methods are particularly attractive within the context of using specialised hardware, such as quantum computers, application specific CMOS and other high performance computing resources for solving optimisation problems. (deepai.org)
These solvers are then applied to QUBO formulations of combinatorial optimisation problems. (deepai.org)
Multi-objective optimisation problems involve finding solutions with var. (deepai.org)
Derive general optimality conditions for convex optimization problems. (warwick.ac.uk)
Apply exact methods for discrete optimization problems with general non-linear convex objective as well heuristics methods. (warwick.ac.uk)
Distinguish between convex and non-convex optimization problems and different solution techniques. (warwick.ac.uk)
Problems in linear programming, quadratic programming, integer programming, nonlinear optimization, systems of dynamic nonlinear equations, and multi-objective optimization can be solved. (apmonitor.com)
All classes of optimization problems are considered. (aiche.org)
Effects of scaling or adding a constant to an objective function and understanding of constrained and unconstrained optimization problems. (freevideolectures.com)
Solution of quadratic programming problems using KKT necessary condition - Basic concept of interior penalties and solution of convex optimization problem via interior point method - Numerical examples are considered to illustrate the techniques mentioned in Lec. (freevideolectures.com)
matrix form of the simplex method - Illustrate the solution of linear programming problems in tabular form via simplex method - Two-phase simplex method - Primal and dual problem: Determination of primal solution from its dual form solution and vice-versa - Properties of dual problems and sensitivity analysis - Basic concept of multi-objective optimization problem and some definitions - Solution of multi-objective optimization problem and illustrate the methodoly with numerical examples. (freevideolectures.com)
Transversality condition - Application of variation approach to control problems - Statement of Linear quadratic regulator (LQR) problem and establish a mathematical framework to solve this problem - Optimal solution of LQR problem - Different techniques for solution of algebraic Riccati equation. (freevideolectures.com)
Solve optimization problems that have a nonlinear objective or are subject to nonlinear constraints. (mathworks.com)
Solve optimization problems that have linear objectives subject to linear constraints with continuous and/or integer variables. (mathworks.com)
Solve optimization problems with quadratic objectives and linear constraints or problems with second-order cone constraints. (mathworks.com)
Solve optimization problems that have multiple objective functions subject to a set of constraints. (mathworks.com)
There are many optimization problems in engineering fields, including shipbuilding. (snu.ac.kr)
To solve such problems, a non-linear optimization program is developed in this study. (snu.ac.kr)
To evaluate the efficiency of the developed program, it was applied to various optimization problems in shipbuilding and the results show that it is applicable to a wide range of optimization problems. (snu.ac.kr)
The book' Chapters identify useful new implementations and ways to integrate and apply the principles of Tabu Search, to hybrid it with others optimization methods, to prove new theoretical results, and to describe the successful application of optimization methods to real world problems. (onlineprogrammingbooks.com)
13 ] proved necessary and sufficient optimality conditions for nondifferential semi-infinite programming problems involving square root of quadratic functions, for more details see [ 14 ]. (ijsmdo.org)
Facility location problems are an important set of problems within the field of optimisation. (tudelft.nl)

In combinatorial optimization, A is some subset of a discrete space, like binary strings, permutations, or sets of integers. (wikipedia.org)

Other applications for data and search engine optimization software incorporate modeling systems, numerical solvers, and general numeric programming plans. (karenabrego.com)
Powell MJD (1994) Advances in Optimization and Numerical Analysis, Kluwer Academic, Dordrecht, A direct search optimization method that models the objective and constraint functions by linear interpolation, pp 51-67. (pyopt.org)
Wrenn G (1989) An indirect method for numerical optimization using the Kreisselmeier-Steinhauser function. (pyopt.org)

modeFRONTIER - an integration platform for multi-objective and multidisciplinary optimization, which provides a seamless coupling with third party engineering tools, enables the automation of the design simulation process, and facilitates analytic decision-making. (wikipedia.org)
Perez R.E., Jansen P.W., and Martins J.R.R.A. (2011) pyOpt: A Python-Based Object-Oriented Framework for Nonlinear Constrained Optimization, Structures and Multidisciplinary Optimization, 45(1):101-118. (pyopt.org)
In: First World Congress of Structural and Multidisciplinary Optimization, Goslar, Germany. (pyopt.org)

The static output feedback synthesis problem is considered under an integral quadratic constraint on the states. (chalmers.se)
The problem is formulated as a multi-objective synthesis in which an H-infinity performance objective is to be guaranteed in addition to the integral quadratic constraint. (chalmers.se)
We propose an off-line optimization of the mentioned problem based on mixed-integer quadratic constraint programming (MIQCP). (sssup.it)

Optimization Toolbox provides functions for finding parameters that minimize or maximize objectives while satisfying constraints. (mathworks.com)

19 ] discussed the optimality and duality for nonsmooth multiobjective fractional programming with generalized convexity. (hindawi.com)

Invited talk at the International Conference on Operations Research, September 2017, Berlin === We present the optimization of the new French standard for keyboard layouts. (slideshare.net)
P.M. Pardalos, A. Žilinskas, J. Žilinskas (2017) Non-Convex Multi-Objective Optimization . (mii.lt)

Collection of interfaces for open source optimization solvers. (scilab.org)
The toolbox includes solvers for linear programming (LP), mixed-integer linear programming (MILP), quadratic programming (QP), second-order cone programming (SOCP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares, and nonlinear equations. (mathworks.com)

We provide conditions ensuring that Pareto optima exist for the Agents using the scalarization method associated with the multi-objective optimization problem and we solve the problem of the Principal by finding optimal remunerations given to the Agents. (repec.org)
We prove under the common assumptions used in direct search for single optimization that at least one limit point of the sequence of iterates generated by DMS lies in (a stationary form of) the Pareto front. (optimization-online.org)
The multi-objective optimization configurations of thickness, the locations of constrained layer damping (CLD) patches for plate are investigated and the vibration characteristics of the CLD/plate are analyzed based on the Pareto optimal solutions. (extrica.com)

It enables you to find optimal solutions in applications such as portfolio optimization, energy management and trading, and production planning. (mathworks.com)

Then we show how, in the absence of explicitly known derivatives, the continuum of Nash equilibria can be calculated approximately via the construction of quadratic surrogate functions. (hal.science)

Problem statement of : convex optimization,quadratic optimization,quadratically constrained quadratic optimization,local and global optima. (freevideolectures.com)

Professor Dazeley is an internationally leading researcher in Multiobjective Reinforcement Learning (MORL) and its application to the Human-alignment problem. (edu.au)
We collected extensive performance data, language statistics, expert ratings on character similarities, and ergonomic scores to implement and solve a multi-objective quadratic assignment problem. (slideshare.net)
We illustrate our study with a linear-quadratic model by comparing the results obtained when we add a Planner in the Principal/multi-Agents problem with the results obtained in the classical second-best case. (repec.org)
Features --------- * fot_linprog: Solves a linear optimization problem. (scilab.org)
fot_intlinprog: Solves a mixed-integer linear optimization problem in intlinprog format with CBC. (scilab.org)
fot_quadprog: Solves a quadratic optimization problem. (scilab.org)
fot_lsqnonneg: Solves a nonnegative linear least squares optimization problem. (scilab.org)
fot_lsqlin: Solves a linear least squares optimization problem. (scilab.org)
fot_lsqnonlin: Solves a nonlinear least squares optimization problem. (scilab.org)
fot_fminunc: Solves an unconstrained optimization problem. (scilab.org)
fot_fminbnd: Solves a nonlinear optimization problem on bounded variables. (scilab.org)
fot_fmincon: Solves a general nonlinear optimization problem. (scilab.org)
fot_fgoalattain: Solves a multiobjective goal attainment problem. (scilab.org)
fot_fminimax: Solves a minimax optimization problem. (scilab.org)
fot_intfminunc: Solves an unconstrained mixed-integer nonlinear optimization problem. (scilab.org)
fot_intfmincon: Solves a constrained mixed-integer nonlinear optimization problem. (scilab.org)
fot_intfminimax: Solves a mixed-integer minimax optimization problem. (scilab.org)
fot_intquadprog: Solves an integer quadratic optimization problem. (scilab.org)
Three approaches of second order mixed type duality are introduced for a nondifferentiable multiobjective fractional programming problem in which the numerator and denominator of objective function contain square root of positive semidefinite quadratic form. (hindawi.com)
Mond [ 25 ] considered a nonlinear fractional programming problem involving square roots of positive semidefinite quadratic form in the numerator and denominator and proved the necessary and sufficient condition for optimality. (hindawi.com)
26 , 27 ] formulated a nondifferentiable multiobjective fractional problem in which numerators contain support function. (hindawi.com)
13 ] to characterize solution of a multiobjective fractional problem under generalized convexity. (hindawi.com)
In this study, we compare methods of deriving scalarisation weights when combining two objectives of the cardinality constrained mean- variance portfolio optimisation problem into one. (deepai.org)
The optimization function is modeled as a multi-objective problem comprising of frequency weighted RMS seat acceleration, Vibration dose value (VDV), RMS suspension space, and RMS tyre deflection. (springeropen.com)
In this study, we use both of these approaches to model a multi-objective facility layout optimization problem depending on a Quadratic Assignment Problem (QAP) formulation. (yildiz.edu.tr)
In this study, we address the visualization of these datasets as a Multi-Objective Optimization Problem. (edu.au)
Our method employs the Multi-Objective Quadratic Assignment Problem (mQAP) as the mathematical foundation to solve the visualization task at hand. (edu.au)
Mod-01 Lec-31 Dynamic Optimization Problem Basic Concepts and Necessary (cont. (freevideolectures.com)
An overview of optimization problem, some examples of optimum design problem - Concepts and terms related to optimization problem, necessary and sufficient conditions for a multivariable function. (freevideolectures.com)
Concept of Lagrange multipliers and its application to unconstrained optimization problem. (freevideolectures.com)
Lecture 31: Mod-01 Lec-31 Dynamic Optimization Problem Basic Concepts and Necessary (cont. (freevideolectures.com)
You can define your optimization problem with functions and matrices or by specifying variable expressions that reflect the underlying mathematics. (mathworks.com)
Model a design or decision problem as an optimization problem. (mathworks.com)
Li Yinong and Xie Ronglu [13] considered the CLD structure optimization as a topology optimization problem, and the evolutionary structural optimization (ESO) method was employed to find the optimal configuration of the CLD patches. (extrica.com)
Can someone please make a list of optimization problem libraries so that the community can add to and refine it? (stackexchange.com)

Gurobi Optimization has secured an "Excellent" Net Promoter Score of 71 for 2023, surpassing B2B industry benchmarks. (gurobi.com)

The toolbox lets you perform design optimization tasks, including parameter estimation, component selection, and parameter tuning. (mathworks.com)

The platform can find optimal solutions, perform trade-off analyses, balance multiple design alternatives, and incorporate optimization methods into external modeling and analysis software. (apmonitor.com)

We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not aggregate any of the objective functions. (optimization-online.org)
Critical essay on the methodology of multiobjective analysis. (iiasa.ac.at)

Search engine optimization is the process of systematically selecting input worth that boost an objective function, such as total bit-width or estimated selection of operators in generated code for a certain system. (pepishairdresser.com)
Search engine optimization is the method of systematically picking input worth that enrich an objective function, such as total bit-width or estimated number of operators in generated code for a particular system. (karenabrego.com)

Artelys Knitro - large scale nonlinear optimization for continuous and mixed-integer programming. (wikipedia.org)

Jansen P, and Perez R (2011) Constrained Structural Design Optimization via a Parallel Augmented Lagrangian Particle Swarm Optimization Approach, International Journal of Computer and Structures, 89(13-14):1352-1366. (pyopt.org)

Application areas: network analysis, cheminformatics (drug design), information visualization, network design and optimization (e.g. (tu-dortmund.de)

Schluter M, Egea J, Banga J (2009) Extended ant colony optimization for non-convex mixed integer nonlinear programming. (pyopt.org)

In this manner, a clear separation of concerns is obtained: different optimization software modules can be easily tested on the same function f, or a given optimization software can be used for different functions f. (wikipedia.org)
Two different optimization strategies are proposed. (extrica.com)

Svanberg K (1987) The method of moving asymptotes - A new method for structural optimization. (pyopt.org)

While the mathematical optimization field is more than 70 years old, many customers are still learning how to make the most of its capabilities. (gurobi.com)

A wide range of exercises and examples are included, illustrating the most widely used optimization methods. (oreilly.com)
The new French keyboard layout is the first modern standard where computational optimization methods were used in interaction with domain experts to implement an optimal keyboard design. (slideshare.net)
DMS generalizes to multiobjective optimization (MOO) all direct-search methods of directional type. (optimization-online.org)
Discrete optimization and exact methods. (warwick.ac.uk)
Optimization Methods and Software 6:265-282. (pyopt.org)

AMPL - modelling language for large-scale linear, mixed integer and nonlinear optimization. (wikipedia.org)
FortMP - linear and quadratic programming. (wikipedia.org)
Excel add-in performs linear, integer, and nonlinear optimization using LINDO. (wikipedia.org)
a non-linear optimization library "EzOptimizer" and a pre-compiler "EzPreCompiler" for the library. (snu.ac.kr)

Carola is associate editor of IEEE Transactions on Evolutionary Computation, ACM Transactions on Evolutionary Learning and Optimization (TELO) and board member of the Evolutionary Computation journal. (sigevo.org)

Anatomy9

Organisms13

Diseases4

Chemicals and Drugs21

Analytical, Diagnostic and Therapeutic Techniques and Equipment82

Phenomena and Processes57

Disciplines and Occupations11

Technology, Industry, Agriculture25

Information Science25

Health Care39

Global optimization9

Algorithm21

Sequential3

Solver5

Engineering design optimization3

Algorithms13

MATLAB7

Solving optimization problems1

Problems30

Combinatorial Optimization1

Numerical3

Multidisciplinary optimization3

Constraint3

Constraints1

Nonsmooth1

20172

Solvers2

Pareto3

Portfolio Optimization1

Surrogate1

Convex optimization1

Problem35

20231

Toolbox1

Incorporate optimization methods1

Methodology2

Search engine optim2

Continuous1

Particle swarm optimi1

Visualization1

Colony Optimization1

Different optimization2

Structural optimization1

Mathematical optimization1

Methods5

Linear4

Evolutionary Computation1