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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: This paper studies two problems which often occur in various applications arising in wireless sensor networks, and provides a diminishing step size algorithm which guarantees asymptotic convergence of the consensus problem and the problem of cooperative solution to a convex optimization problem.
Abstract: In this paper, we study two problems which often occur in various applications arising in wireless sensor networks. These are the problem of reaching an agreement on the value of local variables in a network of computational agents and the problem of cooperative solution to a convex optimization problem, where the objective function is the aggregate sum of local convex objective functions. We incorporate the presence of a random communication graph between the agents in our model as a more realistic abstraction of the gossip and broadcast communication protocols of a wireless network. An added ingredient is the presence of local constraint sets to which the local variables of each agent is constrained. Our model allows for the objective functions to be nondifferentiable and accommodates the presence of noisy communication links and subgradient errors. For the consensus problem we provide a diminishing step size algorithm which guarantees asymptotic convergence. The distributed optimization algorithm uses two diminishing step size sequences to account for communication noise and subgradient errors. We establish conditions on these step sizes under which we can achieve the dual task of reaching consensus and convergence to the optimal set with probability one. In both cases we consider the constant step size behavior of the algorithm and establish asymptotic error bounds.

366 citations

Journal ArticleDOI
TL;DR: This paper investigates the AC-SA algorithms for solving strongly convex stochastic composite optimization problems in more detail by establishing the large-deviation results associated with the convergence rates and introducing an efficient validation procedure to check the accuracy of the generated solutions.
Abstract: In this paper we present a generic algorithmic framework, namely, the accelerated stochastic approximation (AC-SA) algorithm, for solving strongly convex stochastic composite optimization (SCO) problems. While the classical stochastic approximation algorithms are asymptotically optimal for solving differentiable and strongly convex problems, the AC-SA algorithm, when employed with proper stepsize policies, can achieve optimal or nearly optimal rates of convergence for solving different classes of SCO problems during a given number of iterations. Moreover, we investigate these AC-SA algorithms in more detail, such as by establishing the large-deviation results associated with the convergence rates and introducing an efficient validation procedure to check the accuracy of the generated solutions.

366 citations

Book
08 Jul 2014
TL;DR: The authors introduce new material to reflect recent developments in stochastic programming, including an analytical description of the tangent and normal cones of chance constrained sets and in-depth analysis of dynamic risk measures and concepts of time consistency.
Abstract: Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. In Lectures on Stochastic Programming: Modeling and Theory, Second Edition, the authors introduce new material to reflect recent developments in stochastic programming, including: an analytical description of the tangent and normal cones of chance constrained sets; analysis of optimality conditions applied to nonconvex problems; a discussion of the stochastic dual dynamic programming method; an extended discussion of law invariant coherent risk measures and their Kusuoka representations; and in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results. Audience: This book is intended for researchers working on theory and applications of optimization. It also is suitable as a text for advanced graduate courses in optimization.

366 citations

Journal ArticleDOI
TL;DR: In this article, a meta-heuristic of ant colony optimization (ACO) for solving the logistics problem arising in disaster relief activities is presented. But, the problem is not solved in an iterative manner and the results indicate that this algorithm performs well in terms of solution quality and run time.
Abstract: This paper presents a meta-heuristic of ant colony optimization (ACO) for solving the logistics problem arising in disaster relief activities The logistics planning involves dispatching commodities to distribution centers in the affected areas and evacuating the wounded people to medical centers The proposed method decomposes the original emergency logistics problem into two phases of decision making, ie, the vehicle route construction, and the multi-commodity dispatch The sub-problems are solved in an iterative manner The first phase builds stochastic vehicle paths under the guidance of pheromone trails while a network flow based solver is developed in the second phase for the assignment between different types of vehicle flows and commodities The performance of the algorithm is tested on a number of randomly generated networks and the results indicate that this algorithm performs well in terms of solution quality and run time

365 citations

Journal ArticleDOI
TL;DR: A novel scheme is proposed, where optimality is achieved by tracking the necessary conditions of optimality by separating the constraint-seeking from the sensitivity-seeking components of the inputs.

362 citations


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