Computational Optimization and Applications最新文献_第7页

The continuous stochastic gradient method: part I–convergence theory 连续随机梯度法:第一部分收敛理论

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2023-11-23 DOI: 10.1007/s10589-023-00542-8

Max Grieshammer, Lukas Pflug, Michael Stingl, Andrian Uihlein

{"title":"The continuous stochastic gradient method: part I–convergence theory","authors":"Max Grieshammer, Lukas Pflug, Michael Stingl, Andrian Uihlein","doi":"10.1007/s10589-023-00542-8","DOIUrl":"https://doi.org/10.1007/s10589-023-00542-8","url":null,"abstract":"<p>In this contribution, we present a full overview of the <i>continuous stochastic gradient</i> (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function requires some form of integration, e.g., expected values. Since approximating the integration by a fixed quadrature rule can introduce artificial local solutions into the problem while simultaneously raising the computational effort, stochastic optimization schemes have become increasingly popular in such contexts. However, known stochastic gradient type methods are typically limited to expected risk functions and inherently require many iterations. The latter is particularly problematic, if the evaluation of the cost function involves solving multiple state equations, given, e.g., in form of partial differential equations. To overcome these drawbacks, a recent article introduced the CSG method, which reuses old gradient sample information via the calculation of design dependent integration weights to obtain a better approximation to the full gradient. While in the original CSG paper convergence of a subsequence was established for a diminishing step size, here, we provide a complete convergence analysis of CSG for constant step sizes and an Armijo-type line search. Moreover, new methods to obtain the integration weights are presented, extending the application range of CSG to problems involving higher dimensional integrals and distributed data.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Preface to Asen L. Dontchev Memorial Special Issue 阿森·l·顿切夫纪念特刊前言

2区数学

Computational Optimization and Applications Pub Date : 2023-11-03 DOI: 10.1007/s10589-023-00537-5

William W. Hager, R. Tyrrell Rockafellar, Vladimir M. Veliov

引用次数: 0

COAP 2022 Best Paper Prize COAP 2022最佳论文奖

2区数学

Computational Optimization and Applications Pub Date : 2023-10-30 DOI: 10.1007/s10589-023-00538-4

引用次数: 0

Correction to: Stochastic projective splitting 修正为:随机投影分裂

2区数学

Computational Optimization and Applications Pub Date : 2023-10-27 DOI: 10.1007/s10589-023-00539-3

Patrick R. Johnstone, Jonathan Eckstein, Thomas Flynn, Shinjae Yoo

引用次数: 0

A fast continuous time approach for non-smooth convex optimization using Tikhonov regularization technique 基于Tikhonov正则化技术的非光滑凸优化快速连续时间方法

2区数学

Computational Optimization and Applications Pub Date : 2023-10-25 DOI: 10.1007/s10589-023-00536-6

Mikhail A. Karapetyants

引用次数: 0

Optimization over the Pareto front of nonconvex multi-objective optimal control problems 非凸多目标最优控制问题的Pareto前优化

2区数学

Computational Optimization and Applications Pub Date : 2023-10-20 DOI: 10.1007/s10589-023-00535-7

C. Yalçın Kaya, Helmut Maurer

{"title":"Optimization over the Pareto front of nonconvex multi-objective optimal control problems","authors":"C. Yalçın Kaya, Helmut Maurer","doi":"10.1007/s10589-023-00535-7","DOIUrl":"https://doi.org/10.1007/s10589-023-00535-7","url":null,"abstract":"Abstract Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives the Pareto front is usually difficult to view, if not impossible, and even in the case of just two objectives constructing the whole Pareto front so as to visually inspect it might be very costly. Therefore, optimization over the Pareto (or efficient) set has been an active area of research. Although there is a wealth of literature involving finite dimensional optimization problems in this area, there is a lack of problem formulation and numerical methods for optimal control problems, except for the convex case. In this paper, we formulate the problem of optimizing over the Pareto front of nonconvex constrained and time-delayed optimal control problems as a bi-level optimization problem. Motivated by existing solution differentiability results, we propose an algorithm incorporating (i) the Chebyshev scalarization, (ii) a concept of the essential interval of weights, and (iii) the simple but effective bisection method, for optimal control problems with two objectives. We illustrate the working of the algorithm on two example problems involving an electric circuit and treatment of tuberculosis and discuss future lines of research for new computational methods.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135513761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

A new technique to derive tight convex underestimators (sometimes envelopes) 一种推导紧凸低估量(有时是包络)的新技术

2区数学

Computational Optimization and Applications Pub Date : 2023-10-16 DOI: 10.1007/s10589-023-00534-8

M. Locatelli

引用次数: 0

A study of progressive hedging for stochastic integer programming 随机整数规划的渐进式套期保值研究

2区数学

Computational Optimization and Applications Pub Date : 2023-10-11 DOI: 10.1007/s10589-023-00532-w

Jeffrey Christiansen, Brian Dandurand, Andrew Eberhard, Fabricio Oliveira

{"title":"A study of progressive hedging for stochastic integer programming","authors":"Jeffrey Christiansen, Brian Dandurand, Andrew Eberhard, Fabricio Oliveira","doi":"10.1007/s10589-023-00532-w","DOIUrl":"https://doi.org/10.1007/s10589-023-00532-w","url":null,"abstract":"Abstract Motivated by recent literature demonstrating the surprising effectiveness of the heuristic application of progressive hedging (PH) to stochastic mixed-integer programming (SMIP) problems, we provide theoretical support for the inclusion of integer variables, bridging the gap between theory and practice. We provide greater insight into the following observed phenomena of PH as applied to SMIP where optimal or at least feasible convergence is observed. We provide an analysis of a modified PH algorithm from a different viewpoint, drawing on the interleaving of (split) proximal-point methods (including PH), Gauss–Seidel methods, and the utilisation of variational analysis tools. Through this analysis, we show that under mild conditions, convergence to a feasible solution should be expected. In terms of convergence analysis, we provide two main contributions. First, we contribute insight into the convergence of proximal-point-like methods in the presence of integer variables via the introduction of the notion of persistent local minima. Secondly, we contribute an enhanced Gauss–Seidel convergence analysis that accommodates the variation of the objective function under mild assumptions. We provide a practical implementation of a modified PH and demonstrate its convergent behaviour with computational experiments in line with the provided analysis.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136057615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Efficiency of higher-order algorithms for minimizing composite functions 最小化复合函数的高阶算法的效率

2区数学

Computational Optimization and Applications Pub Date : 2023-10-10 DOI: 10.1007/s10589-023-00533-9

Yassine Nabou, Ion Necoara

引用次数: 1

The deepest event cuts in risk-averse optimization with application to radiation therapy design 风险规避优化中的最深事件切割及其在放射治疗设计中的应用

2区数学

Computational Optimization and Applications Pub Date : 2023-10-04 DOI: 10.1007/s10589-023-00531-x

Constantine A. Vitt, Darinka Dentcheva, Andrzej Ruszczyński, Nolan Sandberg

引用次数: 1