Convex combination algorithm. Medical search. Frequent questions

The initial phase of the algorithm formulates the RBF training as a convex optimization problem with an objective function on the expansion weights while the data fitting problem imposed only as an ℓ∞-norm constraint. (nsf.gov)

Let $C$ be their convex hull. (stackexchange.com)
However, the convex hull of a feasible set defined by multiple constraint functions is not completely described by the convex envelope of every single constraint. (springer.com)
In the following, we use the authors' nomination and refer to the convex hull of a set given by multiple constraints as simultaneous convexification. (springer.com)
For a set P of n points in the unit ball b ⊆ R d , consider the problem of finding a small subset T ⊆ P such that its convex-hull ε-approximates the convex-hull of the original set. (nsf.gov)
Specifically, the Hausdorff distance between the convex hull of T and the convex hull of P should be at most ε. (nsf.gov)
First, this work presents a new method to extract lip geometry features using the combination ofa skin colour filter, a border following algorithm and a convex hull approach. (ump.edu.my)
Instead of finding a low-rank subspace to represent the data, we try to represent each data point as a projection to a convex hull of k-points, where the k points themselves are convex combinations of the original data. (neurips.cc)
Summary: Archetypal Analysis (AA) provides a framework in which a dataset is described as a convex combination of prototypes which represent vertices approximating the convex hull of the data. (neurips.cc)

Journal of Algorithms and Computation , 54 (1), 175-186. (ac.ir)
On the resolution of LP-FRE defined by the convex combination operator', Journal of Algorithms and Computation , 54(1), pp. 175-186. (ac.ir)
We have also found that a small subset of the training data that includes the novel data identified by the algorithm can be used to train the non-convex optimization problem with substantial computation savings and comparable errors on the test data. (nsf.gov)
To speed up the computation, our approach exploits a combination of geometric locality, temporal coherence, and predictive methods to compute object-object contacts at kHz rates. (unc.edu)

2} = 1$ are not convex constraints, even though the functions on the left-hand sides are convex. (stackexchange.com)
We state a tractable formulation of the chance constraints using two different methods: A combination of robust and randomized optimization, and an analytical reformulation assuming a Gaussian distribution of the forecast errors. (umich.edu)
To include security constraints, we propose an iterative solution algorithm to recover a feasible solution. (umich.edu)

A large number of sparse signal reconstruction algorithms have been continuously proposed, but almost all greedy algorithms add a fixed number of indices to the support set in each iteration. (scirp.org)
Furthermore, every point of P can be ε- approximated by a convex-combination of points of T that is O(1/ε2 )-sparse. (nsf.gov)
Our result can be viewed as a method for sparse, convex autoencoding: approximately representing the data in a compact way using sparse combinations of a small subset T of the original data. (nsf.gov)
We propose a sequential algorithm for learning sparse radial basis approximations for streaming data. (nsf.gov)
In this work, we first propose a novel spectral-based subspace clustering algorithm that seeks to represent each point as a sparse convex combination of a few nearby points. (cam.ac.uk)

An important step for enabling their solution consists in the design of convex relaxations of the feasible set. (springer.com)
Relaxations are commonly established by convex underestimators, where each constraint function is considered separately. (springer.com)
The practicality of the proposed solution approach is demonstrated on several test instances from gas network optimization, where the method outperforms standard approaches that use separate convex relaxations. (springer.com)
As weak relaxations usually result in a huge number of subproblems and, hence, create branch and bound trees of extremely large sizes, one is interested in constructing the tightest possible convex relaxations leading to smaller branch and bound trees and allowing to find faster good feasible solutions and appropriate branching rules. (springer.com)
In a common approach to derive convex relaxations for MINLPs, the nonlinear functions appearing in the model description are replaced by convex under- and/or concave overestimators. (springer.com)
His research interests include power system operation under uncertainty and convex relaxations of optimal power flow. (umich.edu)

The solution algorithm to this new method is based on iterative convex relaxation. (bvsalud.org)

We present an efficient algorithm to compute such an ε ′ -approximation of size kalg, where ε ′ is a function of ε, and kalg is a function of the minimum size kopt of such an ε-approximation. (nsf.gov)

Birkhoff's algorithm is a greedy algorithm: it greedily finds perfect matchings and removes them from the fractional matching. (wikipedia.org)

Convex optimization: is it possible to find solutions that are exactly feasible and approximately optimal in polynomial time? (stackexchange.com)
A perfect matching in a bipartite graph can be found in polynomial time, e.g. using any algorithm for maximum cardinality matching. (wikipedia.org)
Your work on large scale polynomial optimisation, which combines novel theory of algebraic geometry and convex optimisation, will lay a solid mathematical foundation for novel computational methods in polynomial optimisation. (edu.au)
The mathematical methods and algorithms used for polynomial problems of large size are not sufficiently developed, limiting their applicability for real-world problems. (edu.au)
Being new to the OR and Optimization world, I've always assumed that a problem being convex meant that it can be solved in polynomial time. (stackexchange.com)
On the other hand, This lecture from a Stanford Professor, around 28:00 states that convexity means tractability and polynomial time algorithms. (stackexchange.com)
There are special cases of convex problems that can be solved in polynomial time, e.g. a convex QP defined over a simplex. (stackexchange.com)

Such mechanisms, which are examples of general global optimization methods, include simulated annealing and genetic algorithms . (wikipedia.org)
This article presents a Genetic Algorithm that searches for the shortest path to visit many places and return to the original one. (fastly.net)
I recently published the article An alternative introduction to Genetic and Evolutionary Algorithms , in which I presented an Evolutionary Algorithm that's capable of finding some math formulas. (fastly.net)
Those are all traits used by the Genetic Algorithms , yet my sample was not a Genetic Algorithm because it didn't used chromosomes and genes . (fastly.net)
Well, this time I will present a real genetic algorithm with the purpose of solving the Travelling Salesman Problem (often presented simply as TSP). (fastly.net)
Maybe the most important trait to have a Genetic Algorithm is the analogy to biology that requires the use of chromosomes and, consequently, the use of genes. (fastly.net)

The surrogate optimization algorithm alternates between two phases. (mathworks.com)
The surrogate optimization algorithm description uses the following definitions. (mathworks.com)

In particular, we apply the method to quadratic absolute value functions and derive their convex envelopes. (springer.com)

One such application is for the problem of fair random assignment: given a randomized allocation of items, Birkhoff's algorithm can decompose it into a lottery on deterministic allocations. (wikipedia.org)
In order to efficiently reconstruct the original signal, a lot of algorithms have been proposed to solve this problem. (scirp.org)
So the problem can be solved by the l 0 norm minimization, which is an NP-hard problem [14] that requires exhaustively listing all possibilities of the original signal and is difficult to achieve by the traditional algorithm. (scirp.org)
We introduce a separation method that relies on determining the convex envelope of linear combinations of the constraint functions and on solving a nonsmooth convex problem. (springer.com)
An algorithm to explore the candidate stabilizing controller actions is proposed and an application to an automotive engine control problem is described. (unipi.it)
In particular, we describe efficient algorithms for learning a maximum alignment kernel by showing that the problem can be reduced to a simple QP and discuss a one-stage algorithm for learning both a kernel and a hypothesis based on that kernel using an alignment-based regularization. (nyu.edu)
Based on some structural properties of the problem, an algorithm is presented to find the optimal solutions and finally, an example is described to illustrate the algorithm. (ac.ir)
EDIT: As per @Geoff Oxberry, the problem is not convex. (stackexchange.com)
Your problem is not convex. (stackexchange.com)
begingroup$ I've thought about it, and have come to the conclusion that indeed the problem is not generally convex, but really the weirdness is that $(h_1,h_2)=(g_1,g_1)$ is actually a maximum . (stackexchange.com)
For each instance I of a problem, let OPT(I) denote the value of an optimal solution to instance I. We say that an algorithm A is an α-approximation algorithm for a problem if, for every instance I, the value of the feasible solution returned by A is within a (multiplicative) factor of α of OPT(I). Equivalently, we say that A is an approximation algorithm with approximation ratio α. (dokumen.pub)
The approximation ratio of an algorithm for a minimization problem is the maximum (or supremum), over all instances of the problem, of the ratio between the values of solution returned by the algorithm and the optimal solution. (dokumen.pub)
For example, an algorithm has an α-approximation for a minimization problem if it outputs a feasible solution of value at most OPT(I) + α for all I. This is a valid definition and is the more relevant one in some settings. (dokumen.pub)
Numerical experiments on an image restoration problem show that the combination of the ``warm--start'' strategy with an appropriate choice of the inertial parameters is strictly required in order to guarantee the convergence to the real minimum point of the objective function. (optimization-online.org)
While graph drawing can be a difficult problem, force-directed algorithms, being physical simulations, usually require no special knowledge about graph theory such as planarity . (wikipedia.org)
When there is no restriction on P, we show the problem can be reduced to APSP in an unweighted directed graph, yielding an O(n^2.5302) time algorithm when minimizing k and an O(min{n^2.5302, kn^2.376}) time algorithm when minimizing ε, using prior results for APSP. (nsf.gov)
The second phase of the algorithm involves a non-convex refinement of the convex problem. (nsf.gov)
Inspired by these ideas, the problem of recovering a low-rank matrix from an incomplete sampling subset of its entries with an unknown fraction of the samplings contaminated by arbitrary errors was considered, which was defined as a problem of matrix completion from corrupted samplings and modeled as a convex optimization problem that minimizes a combination of the nuclear norm and the l 1 -norm in this paper. (dqxxkx.cn)
Meanwhile, a novel and effective algorithm called augmented subsection Lagrange multipliers was put forward to exactly solve the problem. (dqxxkx.cn)
If a convex optimization problem can be NP-Hard, in what sense are convex problems easier than non-convex problems? (stackexchange.com)
Now I am learning that a convex optimization problem can be NP-Hard, but that convex problems are still somehow considered easier than non-convex problems. (stackexchange.com)
What I call an NP-harder problem is one that requires the combination of numerous NP-hard algorithms to solve, sometimes evoking each other exponentially many times. (stackexchange.com)
In fact, solving a mixed integer convex problem is usually much harder than solving a nonconvex NLP to local optimality. (stackexchange.com)

3. To build a toolkit of broadly applicable algorithms/heuristics that can be used to solve a variety of problems. (dokumen.pub)
That is, it is unlikely that there exist algorithms to solve NP optimization problems efficiently, and so we often resort to heuristic methods to solve these problems. (dokumen.pub)
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)

Recommended books: - The Design of Approximation Algorithms by David Shmoys and David Williamson, Cambridge University Press, coming in 2011. (dokumen.pub)
Approximation Algorithms by Vijay Vazirani, Springer-Verlag, 2004. (dokumen.pub)
2. To learn techniques for design and analysis of approximation algorithms, via some fundamental problems. (dokumen.pub)

C.Y. Chong and S. Mori, "Convex combination and covariance intersection algorithms in distributed fusion", Proceedings of the 4th International Conference of Information Fusion, Montreal, QC, Canada, pp.WeA2.11-WeA2.18, 2001. (ejournal.org.cn)

The dual simplex algorithm is applied to determine a new optimal solution. (nsf.gov)
The structure of the simplex algorithm makes the update to the solution particularly efficient given the inverse of the new basis matrix is easily computed from the old inverse. (nsf.gov)

With that in mind, there are two main classes of convex problems: (i) continuous and (ii) mixed integer. (stackexchange.com)
For mixed integer convex problems, we need to use methods such as branch-and-bound, so intuitively we can see why this is NP-hard and difficult in practice. (stackexchange.com)

Abstract This study proposes an efficient algorithm for improving flattening result of triangular mesh surface patches having a convex shape. (techscience.com)
abstract = "This paper presents new and effective algorithms for learning kernels. (nyu.edu)
Abstract: We present an algorithm for haptic display of moderately complex polygonal models with a six degree of freedom (DOF) force feedback device. (unc.edu)

begingroup$ Gradient descent works for convex problems, but not for non-convex problems. (stackexchange.com)

Simulation results demonstrate the proposed algorithm significantly outperforms the CoSaMP for image recovery and one-dimensional signal. (scirp.org)

For each subproblem, a convex relaxation of the feasible set is generated, providing lower bounds for the original subproblem, where the quality of these bounds depends on the tightness of the relaxation. (springer.com)
Our theoretical results include a novel concentration bound for centered alignment between kernel matrices, the proof of the existence of effective predictors for kernels with high alignment, both for classification and for regression, and the proof of stability-based generalization bounds for a broad family of algorithms for learning kernels based on centered alignment. (nyu.edu)
To construct the surrogate, the algorithm chooses quasirandom points within the bounds. (mathworks.com)

For these problems, when P is in convex position, we respectively give an O(n log²n) time algorithm and an O(n log³n) time algorithm, where the latter running time holds with high probability. (nsf.gov)
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)

How to prove that a given class of convex programs cannot be solved by linear programming? (stackexchange.com)
PSDBoost is based on the observation that any trace-one positive semidefinitematrix can be decomposed into linear convex combinations of trace-one rank-one matrices, which serve as base learners of PSDBoost. (nips.cc)
Identifying the distribution of linear combinations of gamma random variables via Stein's method. (dlut.edu.cn)
Finally, we show our near linear algorithms for convex position give 2-approximations for the general case. (nsf.gov)
An efficient algorithm for optimal linear estimation fusion in distributed multisensor systems", IEEE Trans. (ejournal.org.cn)
PLS explores the linear combination of spectral data and chemical composition. (vision-systems.com)

Our algorithm is mainly inspired by LPBoost [1] and the general greedy convex optimization framework of Zhang [2]. (nips.cc)
This optimal treatment computational modeling framework can be applied to other single and combination treatments for both prediction and optimization, as well as incorporate new clinical trial data as it becomes available. (plos.org)
We then extend the algorithm to a constrained clustering and active learning framework. (cam.ac.uk)

The main idea of the Branch and Bound algorithm is to generate a tree structure of subproblems that arise from a subdivision of the feasible set. (springer.com)

Instead, a considerably tighter relaxation can be found via so-called simultaneous convexification, where convex underestimators are derived for more than one constraint function at a time. (springer.com)

In 31st Annual European Symposium on Algorithms (ESA 2023). (dagstuhl.de)

And without increasing the computational complexity, the proposed improvement algorithm has a higher exact reconstruction rate and peak signal to noise ratio (PSNR). (scirp.org)
Computational visual perception seeks to reproduce human vision through the combination of visual sensors, artificial intelligence and computing. (hal.science)

The easiest way to picture this in a simpler case is to note that the unit circle (or sphere) is not a convex set because the line between any two points on the circle (or sphere) is not contained in the set. (stackexchange.com)

Different simulation results show that the improved algorithm has better reconstruction performance for both one-dimensional signals and two-dimensional signals compared with other classical algorithms. (scirp.org)
Mapping results of the proposed algorithm and the base technique are compared by area and shape accuracy metrics measured for several sample surfaces. (techscience.com)
Most of these results have in common that they analyze the convex envelope of a single real-valued function. (springer.com)
In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to improve upon in the past, as well as other algorithms for learning kernels based on convex combinations of base kernels in both classification and regression. (nyu.edu)
We also report the results of experiments with our centered alignment-based algorithms in both classification and regression. (nyu.edu)
Modularity, scalability and portability are the main strength of these methods which once combined with eﬃcient inference algorithms they could lead to state of the art results. (hal.science)
Nevertheless, they consti- tute two complementary importance sampling strategies of transported light and as we show, their combination yields superior results to each strategy alone. (9pdf.net)

1] J. C. Bezdek, "Pattern Recognition with Fuzzy Objective Function Algorithms," Plenum Press, 1981. (fujipress.jp)
The algorithm evaluates the objective function at these points. (mathworks.com)
The algorithm constructs a surrogate as an interpolation of the objective function by using a radial basis function (RBF) interpolator. (mathworks.com)

We propose a nested primal--dual algorithm with extrapolation on the primal variable suited for minimizing the sum of two convex functions, one of which is continuously differentiable. (optimization-online.org)
The proposed algorithm can be interpreted as an inexact inertial forward--backward algorithm equipped with a prefixed number of inner primal--dual iterations for the proximal evaluation and a ``warm--start'' strategy for starting the inner loop, and generalizes several nested primal--dual algorithms already available in the literature. (optimization-online.org)

On one hand, based on this post and the accepted answer , yes, There are examples of convex optimization problems which are NP-hard. (stackexchange.com)
If it is indeed true that convex optimization problems can be NP-Hard, then in what sense are they "easier" than non-convex problems? (stackexchange.com)
I frequently hear Operations Research people say that we have all sorts of tools for convex problems, while non-convex problems are still very hard to deal with? (stackexchange.com)
Tractability of convex problems essentially boils down to being able to decide if a solution $x$ is feasible, in a computationally tractable way (having a so called oracle available). (stackexchange.com)

fuzzy c -varieties and convex combinations thereof," SIAM J. Appl. (fujipress.jp)
In this type of FRE, fuzzy composition is considered as the convex combination operator. (ac.ir)

We demonstrate the essence of the algorithm, termed PSDBoost (positive semidefinite Boosting), by focusing on a few different applications in machine learning. (nips.cc)
We demonstrate its performance on force display of the mechanical interaction between moderately complex geometric structures that can be decomposed into convex primitives. (unc.edu)

However, the effects of multicollinearity can only be reduced but not completely removed by PLS, but variable selection methods such as successive projections algorithm prove effective by selecting subsets of variables with minimum redundancy and collinearity. (vision-systems.com)

If the sampled signal has sparsity or compressibility, the original signal can be recovered well by sampling only a small number of data points and selecting the reconstruction algorithm reasonably. (scirp.org)
During the Construct Surrogate phase, the algorithm constructs sample points from a quasirandom sequence. (mathworks.com)

Bilinear terms are known not to be convex, and I doubt that composing them with a 2-norm changes the non-convexity. (stackexchange.com)

A synthesis methodology is obtained by extending to hybrid systems the stabilization techniques based on stable convex combinations, originally developed for switching systems. (unipi.it)

In 1960, Joshnson, Dulmage and Mendelsohn showed that Birkhoff's algorithm actually ends after at most n2 − 2n + 2 steps, which is tight in general (that is, in some cases n2 − 2n + 2 permutation matrices may be required). (wikipedia.org)
In general, however, convex programming is NP-hard. (stackexchange.com)

This procedure is now done for each combination of variety, grade, and growing region. (vision-systems.com)
Algorithm 2 provides the coreset C and the query Q consists of the archetypes z_1, …, z_k which are initialised with the FurthestSum procedure. (neurips.cc)

propose an algorithm to learn in batch reinforcement learning (RL), a setting where an agent learns purely form a fixed batch of data, $B$, without any interactions with the environments. (shortscience.org)

Hence, a broad field of research is devoted to finding the tightest possible convex under- and concave overestimators (the so-called convex and concave envelopes ) for different types of relevant functions. (springer.com)
I'm a little perplexed as all functions are convex in each variable, but I'm no expert in NLP. (stackexchange.com)
The involved functions are convex in each single variable, but maybe not overall. (stackexchange.com)

We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. (openreview.net)

The dynamic virtual boundary approach is utilized to reduce the distortions for the triangles near the boundary caused by the nature of convex combination technique. (techscience.com)

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

Sequential Maximum Convex Cone Endmember Model (SMACC) was used as the spectral feature extraction method. (vision-systems.com)

Based on the full study of the theory of compressed sensing, we propose a dynamic indexes selection strategy based on residual update to improve the performance of the compressed sampling matching pursuit algorithm (CoSaMP). (scirp.org)

these algorithms have low reconstruction complexity but require more measurements to perfect reconstruction. (scirp.org)

Chemicals and Drugs2

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