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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


Papers
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Journal ArticleDOI
TL;DR: A general classification of mathematical optimization problems is provided, followed by a matrix of applications that shows the areas in which these problems have been typically applied in process systems engineering.

566 citations

Book
01 Jan 1986
TL;DR: The solution of Large-scale Programming Problems: Generalized Linear Programming and Decomposition Techniques Dynamic Programming Optimization in Infinite Dimension and Applications is presented.
Abstract: Preface Foreword Notation Fundamental Concepts Linear Programming One-dimensional Optimization Nonlinear, Unconstrained Optimization Nonlinear Optimization with Constraints Nonlinear Constrained Optimization Integer Programming Solution of Large-scale Programming Problems: Generalized Linear Programming and Decomposition Techniques Dynamic Programming Optimization in Infinite Dimension and Applications References Appendices Index.

564 citations

Journal ArticleDOI
TL;DR: A collection of test problems, some are better known than others, provides an easily accessible collection of standard test problems for continuous global optimization and investigates the microscopic behavior of the algorithms through quartile sequential plots.
Abstract: There is a need for a methodology to fairly compare and present evaluation study results of stochastic global optimization algorithms. This need raises two important questions of (i) an appropriate set of benchmark test problems that the algorithms may be tested upon and (ii) a methodology to compactly and completely present the results. To address the first question, we compiled a collection of test problems, some are better known than others. Although the compilation is not exhaustive, it provides an easily accessible collection of standard test problems for continuous global optimization. Five different stochastic global optimization algorithms have been tested on these problems and a performance profile plot based on the improvement of objective function values is constructed to investigate the macroscopic behavior of the algorithms. The paper also investigates the microscopic behavior of the algorithms through quartile sequential plots, and contrasts the information gained from these two kinds of plots. The effect of the length of run is explored by using three maximum numbers of function evaluations and it is shown to significantly impact the behavior of the algorithms.

545 citations

Journal ArticleDOI
TL;DR: This paper describes a multicut algorithm to carry out outer linearization of stochastic programs and presents experimental and theoretical justification for reductions in major iterations.

532 citations

Journal ArticleDOI
TL;DR: The accelerated stochastic approximation (AC-SA) algorithm based on Nesterov’s optimal method for smooth CP is introduced, and it is shown that the AC-SA algorithm can achieve the aforementioned lower bound on the rate of convergence for SCO.
Abstract: This paper considers an important class of convex programming (CP) problems, namely, the stochastic composite optimization (SCO), whose objective function is given by the summation of general nonsmooth and smooth stochastic components. Since SCO covers non-smooth, smooth and stochastic CP as certain special cases, a valid lower bound on the rate of convergence for solving these problems is known from the classic complexity theory of convex programming. Note however that the optimization algorithms that can achieve this lower bound had never been developed. In this paper, we show that the simple mirror-descent stochastic approximation method exhibits the best-known rate of convergence for solving these problems. Our major contribution is to introduce the accelerated stochastic approximation (AC-SA) algorithm based on Nesterov’s optimal method for smooth CP (Nesterov in Doklady AN SSSR 269:543–547, 1983; Nesterov in Math Program 103:127–152, 2005), and show that the AC-SA algorithm can achieve the aforementioned lower bound on the rate of convergence for SCO. To the best of our knowledge, it is also the first universally optimal algorithm in the literature for solving non-smooth, smooth and stochastic CP problems. We illustrate the significant advantages of the AC-SA algorithm over existing methods in the context of solving a special but broad class of stochastic programming problems.

531 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532