Convex optimization. Medical search. Frequent questions

Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard. (wikipedia.org)
With recent advancements in computing and optimization algorithms, convex programming is nearly as straightforward as linear programming. (wikipedia.org)
Besides the usually simple description and implementation of OCO algorithms, a lot of this recent success is due to a deepening of our understanding of the OCO setting and their algorithms by using cornerstone ideas from convex analysis and optimization such as the powerful results from convex duality theory. (ubc.ca)
With respect to algorithms for OCO, we first present and analyze the Adaptive Follow the Regularized Leader (AdaFTRL) together with an analysis which relies mainly on the duality between strongly convex and strongly smooth functions. (ubc.ca)
In this paper, we introduce basic bandit optimization algorithms and explain their performance. (ieice.org)
We overcome this challenge by designing normalized gradient descent-based algorithms and showed near-optimal convergence rates for smooth and strongly convex functions. (ucla.edu)
Aadirupa obtained her P.h.D from the department of Computer Science, Indian Institute of Science, Bangalore, advised by Aditya Gopalan and Chiranjib Bhattacharyya and interned at Microsoft Research, INRIA Paris, and Google AI.Her research interests include Bandits, Reinforcement Learning, Optimization, Learning theory, Algorithms. (ucla.edu)
In this course, we will cover theory and algorithms for convex optimization. (jhu.edu)
We will then explore a diverse array of algorithms to solve convex optimization problems in a variety of applications, such as gradient methods, sub-gradient methods, accelerated methods, proximal algorithms, Newton's method, and ADMM. (jhu.edu)
This course is designed to give a graduate-level student a thorough grounding in these properties and their role in optimization, and a broad comprehension of algorithms tailored to exploit such properties. (freevideolectures.com)
We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. (mlr.press)
As a consequence, several works in theoretical computer science, machine learning and optimization have focused on coming up with polynomial time algorithms to minimize F under conditions on the noise F(x)-F̂(x) such as its uniform-boundedness, or on F such as strong convexity. (deepai.org)
Analyzing such an algorithm for the unbounded noise model and a general convex function turns out to be challenging and requires several technical ideas that might be of independent interest in deriving non-asymptotic bounds for other simulated annealing based algorithms. (deepai.org)
We constrict our comparison in two types of the above L0-norm solutions: greedy algorithms and convex L1-norm solutions. (ku.dk)
We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. (openreview.net)

The focus will be on convex optimization problems (though we also may touch upon nonconvex optimization problems at some points). (freevideolectures.com)
We introduce a generic scheme to solve nonconvex optimization problems u. (deepai.org)

To solve the problem, optimization methods without the derivative have been developed in recent years. (ieice.org)
Instead, we use minimax duality to reduce the problem to a Bayesian setting, where the convex loss functions are drawn from a worst-case distribution, and then we solve the Bayesian version of the problem with a variant of Thompson Sampling. (videolectures.net)
How to solve the following continuous optimization problem? (stackexchange.com)
This course focuses on the practical aspects of using convex optimization methods to solve these problems. (umich.edu)
As we obviously cannot solve every problem in machine learning, this means that we cannot generically solve every optimization problem (at least not efficiently). (freevideolectures.com)
Convex.jl makes it easy to describe optimization problems in a natural, mathematical syntax, and to solve those problems using a variety of different (commercial and open-source) solvers. (readthedocs.io)
A first order approximation is that convex programs are tractable, .i.e., most problems you can think of as a layman in the field that are convex, are (probably) tractable to solve. (stackexchange.com)
RANSAC), which enables us to solve non-convex optimization problems by in- stead solving many subproblems. (lu.se)
The model is non-linear and non-convex and therefore harder to solve which prompted us to also consider a modification of this model which can be transformed into a linear programming model that can be solved more efficiently. (cdc.gov)

Convex.jl is a Julia package for Disciplined Convex Programming . (readthedocs.io)

Such methods are called bandit optimization methods in the machine learning community. (ieice.org)
We analyze the minimax regret of the adversarial bandit convex optimization problem. (videolectures.net)
Our results simultaneously generalize online boosting and gradient boosting guarantees to contextual learning model, online convex optimization and bandit linear optimization settings. (icml.cc)

The feasible set C {\displaystyle C} of the optimization problem consists of all points x ∈ D {\displaystyle \mathbf {x} \in {\mathcal {D}}} satisfying the constraints. (wikipedia.org)
Nearly every problem in machine learning and computational statistics can be formulated in terms of the optimization of some function, possibly under some set of constraints. (freevideolectures.com)
My objective and constraints are infinitely differentiable but not necessarily convex. (stackexchange.com)
I tried doing some reading about this online but a lot of sources I see focus on the case where the objective and constraints are convex. (stackexchange.com)
The primary focus is on a problem of maximizing a concave functional of the field subject to a system of convex and linear constraints. (manchester.ac.uk)
For non-convex obstacle constraints, we propose an algorithm that generates up to two alternative linear constraints to convexify the obstacle constraints for improving computational efficiency. (asme.org)
Other places seem to consider problems where if aside from the integer constraint, all other constraints and the objective function are convex, to be convex optimization problems. (stackexchange.com)

In it's general form (when state transition dynamics are unknown), learning LDS is a classic non-convex problem, typically tackled with heuristics like gradient descent ("backpropagation through time") or the EM algorithm. (rutgers.edu)
In this access model, we give an efficient boosting algorithm that guarantees near-optimal regret against the convex hull of the base class. (icml.cc)
To this end, we propose an asynchronous distributed algorithm, named Asynchronous Single-looP alternatIve gRadient projEction (ASPIRE) algorithm with the itErative Active SEt method (EASE) to tackle the distributed distributionally robust optimization (DDRO) problem. (nips.cc)
In this paper, we propose an accelerated stochastic step search algorithm which combines an accelerated method with a fully adaptive step size parameter for convex problems in (Scheinberg et. (ibm.com)
To fill in these gaps, this paper proposes a novel Directly Accelerated stochastic Variance reductIon (DAVIS) algorithm with two Snapshots for non-strongly convex (non-SC) unconstrained problems. (icml.cc)
Turning our result on its head, one may also view our algorithm as minimizing a nonconvex function F̂ that is promised to be related to a convex function F as above. (deepai.org)
An efficient algorithm for solv- ing the resulting optimization problem is devised exploiting a novel variable step-size alternating direction method of multipliers (ADMM). (lu.se)

Distributionally Robust Optimization (DRO), which aims to find an optimal decision that minimizes the worst case cost over the ambiguity set of probability distribution, has been applied in diverse applications, e.g., network behavior analysis, risk management, etc. (nips.cc)

Many optimization problems can be equivalently formulated in this standard form. (wikipedia.org)
DECOPT is a MATLAB software package for the generic constrained convex optimization problems. (epfl.ch)
In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality conditions for constraint optimization problems in terms of the Dini derivative are given. (optimization-online.org)
Convex optimization plays a central role in the numerical solution of many design and analysis problems in control theory. (umich.edu)
Fortunately, many problems of interest in machine learning can be posed as optimization tasks that have special propertiessuch as convexity, smoothness, sparsity, separability, etc.permitting standardized, efficient solution techniques. (freevideolectures.com)
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. (nips.cc)
The paper analyzes stochastic optimization problems involving random fields on infinite directed graphs. (manchester.ac.uk)
His current research interests are focused on data-driven optimization, the development of efficient computational methods for the solution of stochastic and robust optimization problems and the design of approximation schemes that ensure their computational tractability. (epfl.ch)
Presenting classical approximations and modern convex relaxations side-by-side, and a selection of problems and worked examples, this is an invaluable resource for students and researchers from industry and academia in power systems, optimization, and control. (njit.edu)
In this video, starting at 27:00 , Stephen Boyd from Stanford claims that convex optimization problems are tractable and in polynomial time. (stackexchange.com)
I can't wrap my head around the two statements, are convex optimization problems tractable or not? (stackexchange.com)
As I try to dig deeper, one thing I noticed it that the term convex doesn't seem to be used the same way by different people when it comes to integer problems. (stackexchange.com)
If it is possible for an integer programming problem to be convex, then in what sense are convex optimization problems "easier" that non-convex problems, since both are NP-Hard? (stackexchange.com)
Feels like you are asking two things, tractability of convex problems and convexity of integer problems. (stackexchange.com)
Tractability of convex problems essentially boils down to being able to decide if an iterate $x$ is feasible, in a computationally tractable way (having a so called oracle available). (stackexchange.com)
A novel method is presented and explored within the framework of Potts neural networks for solving optimization problems with a non-trivial topology, with the airline crew scheduling problem as a target application. (lu.se)
The method is explored on a set of synthetic dealt with in a straightforward way using ``stan- problems, which are generated to resemble two dard'' ANN energy functions similar to those en- real-world problems representing long and medi- countered in spin physics. (lu.se)
In this paper, an improved Interior-Point Method (IPM) for solving symmetric optimization problems is presented. (cdc.gov)
Symmetric optimization (SO) problems are linear optimization problems over symmetric cones. (cdc.gov)

A convex optimization problem is an optimization problem in which the objective function is a convex function and the feasible set is a convex set. (wikipedia.org)
It is known that the curvature of the feasible set in convex optimizatio. (deepai.org)
By some definitions, it seems that a convex integer optimization problem is impossible by definition: the very fact of constraining the variables to integer values removes the convexity of the problem, since for a problem to be convex, both the objective function and the feasible set have to be convex. (stackexchange.com)
Or is it non-convex by definition, given the restrictions it puts on the feasible set? (stackexchange.com)

In the theory of convex optimization, the derivative of the objective function including the gradient and the Hessian is typically used to search the optimum point. (ieice.org)
In machine learning and optimization, one often wants to minimize a convex objective function F but can only evaluate a noisy approximation F̂ to it. (deepai.org)

who assume that the noise grows in a very specific manner and that F is strongly convex. (deepai.org)

Convex optimization has applications in a wide range of disciplines, such as automatic control systems, estimation and signal processing, communications and networks, electronic circuit design, data analysis and modeling, finance, statistics (optimal experimental design), and structural optimization, where the approximation concept has proven to be efficient. (wikipedia.org)

As an application of ARC, an evaluation on the effectiveness of the stochastic gradient descent in a non-convex setting is also described. (arxiv.org)

Abstract We introduce a model-based excessive gap technique to analyze first-order primal- dual methods for constrained convex minimization. (epfl.ch)
abstract = "Optimization is ubiquitous in power system engineering. (njit.edu)

Online Convex Optimization (OCO) is a field in the intersection of game theory, optimization, and machine learning which has been receiving increasing attention due to its recent applications to a wide range of topics such as complexity theory and graph sparsification. (ubc.ca)
We will conclude the talk with a plethora of open questions led by this general direction of optimization with `unconventional feedback' which can help bridging the gaps between theory and practice in many real-world applications. (ucla.edu)

A Primal-Dual Algorithmic Framework for Constrained Convex Minimization" , LIONS Tech. Report EPFL-REPORT-199844 , (2014). (epfl.ch)

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). (wikipedia.org)
If f {\displaystyle f} is unbounded below over C {\displaystyle C} or the infimum is not attained, then the optimization problem is said to be unbounded. (wikipedia.org)
A solution to a convex optimization problem is any point x ∈ C {\displaystyle \mathbf {x} \in C} attaining inf { f ( x ) : x ∈ C } {\displaystyle \inf\{f(\mathbf {x} ):\mathbf {x} \in C\}} . In general, a convex optimization problem may have zero, one, or many solutions. (wikipedia.org)
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. (epfl.ch)
I encounter an optimization problem. (stackexchange.com)
Drawing on powerful, modern tools from convex optimization, this rigorous exposition introduces essential techniques for formulating linear, second-order cone, and semidefinite programming approximations to the canonical optimal power flow problem, which lies at the heart of many different power system optimizations. (njit.edu)
Can an integer optimization problem be convex? (stackexchange.com)
Other sources state that a convex optimization problem can be NP-hard. (stackexchange.com)
Regarding the second issue whether an integer problem is convex, the answer is no, and that follows directly from geometry (unless there is only 1 solution). (stackexchange.com)
Remember from the discussion above though, this only implies we've made a convex reformulation, not that the problem has been made tractable. (stackexchange.com)

We show that combining momentum, normalization, and gradient clipping allows for high-probability convergence guarantees in non-convex stochastic optimization even in the presence of heavy-tailed gradient noise. (openreview.net)

He is the editor-in-chief of Mathematical Programming and the area editor for continuous optimization for Operations Research. (epfl.ch)

Let $C$ be their convex hull. (stackexchange.com)

Evstigneev, IV & Taksar, MI 2001, ' Convex stochastic optimization for random fields on graphs: A method of constructing Lagrange multipliers ', Mathematical Methods of Operations Research , vol. 54, no. 2, pp. 217-237. (manchester.ac.uk)

This set is convex because D {\displaystyle {\mathcal {D}}} is convex, the sublevel sets of convex functions are convex, affine sets are convex, and the intersection of convex sets is convex. (wikipedia.org)
Our analysis features a novel use of convexity, formalized as a ``local-to-global'' property of convex functions, that may be of independent interest. (videolectures.net)

Convex.jl supports many solvers, including Mosek , Gurobi , ECOS , SCS and GLPK , through the MathProgBase interface. (readthedocs.io)
I am calling Mosek and SCS through Convex.jl and want to track how quickly these solvers are converging (for plotting purposes). (julialang.org)

Our primary technique is a reduction from non-smooth non-convex optimization to online learning , after which our results follow from standard regret bounds in online learning. (mlr.press)

How to prove that a given class of convex programs cannot be solved by linear programming? (stackexchange.com)
The recommended subroutine lp() is a linear program solver ( simplex method ) from Matlab's Optimization Toolbox v2.0 (R11). (convexoptimization.com)

In this talk, I will present a quantitative single-particle and single-cell imaging platform called CLiC (Convex Lens-induced Confinement) which we have developed and applied to fill important gaps in understanding and characterization of nanomedicines and thereby help make them better. (lu.se)

Slope - adaptive variable selection via convex optimization. (lu.se)

We consider the decision-making framework of online convex optimization with a very large number of experts. (icml.cc)

We develop a reduction from robust improper optimization to stochastic optimization: given an oracle that returns $\alpha$-approximate solutions for distributions over objectives, we compute a distribution over solutions that is $\alpha$-approximate in the worst case. (nips.cc)

Denote function $F(x):\mathbf{R}^n\rightarrow\mathbf{R}$, where $F(x)$ is a smooth lower bounded convex function (i.e. (stackexchange.com)

We apply our results to robust neural network training and submodular optimization. (nips.cc)

However, as shown by Sam Burer, nononvex mixed-binary quadratic programs can be rewritten as convex optimization over the co-positive cone. (stackexchange.com)

Two types of convex relaxations have recently been proposed for the tensor multilinear rank. (neurips.cc)

But for general smooth, lower bounded, convex function, do we also have the result correct? (stackexchange.com)

There are convex sets for which this isn't the case. (stackexchange.com)

Applied Mathematics, Optimization. (ac.ir)

Daniel Kuhn is Professor of Operations Research at the College of Management of Technology at EPFL, where he holds the Chair of Risk Analytics and Optimization (RAO). (epfl.ch)

Convex optimization is at the heart of many disciplines such as machine learning, signal processing, control, medical imaging, etc. (jhu.edu)

We first describe the online learning and online convex optimization settings, proposing an alternative way to formalize both of them so we can make formal claims in a clear and unambiguous fashion while not cluttering the readers understanding. (ubc.ca)

Phenomena and Processes1

Information Science2

Algorithms15

Nonconvex optimization problems2

Solve9

Disciplined Convex Programming1

Bandit3

Constraints7

Algorithm7

Distributionally robust optimization1

Problems19

Feasible set4

Objective function2

Strongly1

Approximation1

Stochastic gradien1

Abstract2

Theory2

Minimization1

Problem10

Convergence1

Continuous optimization1

Hull1

20011

Functions2

Mosek2

Regret1

Linear2

Gaps1

Adaptive1

Framework1

Objectives1

Mathbf1

Neural1

Cone1

Relaxations1

Function1

Sets1

Mathematics1

Operations Research1

Control1

Describe1