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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: The rate of convergence of the SBMD method along with its associated large-deviation results for solving general nonsmooth and stochastic optimization problems and some of the results seem to be new for block coordinate descent methods for deterministic optimization.
Abstract: In this paper, we present a new stochastic algorithm, namely, the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate block coordinate decomposition and an incremental block averaging scheme into the classic (stochastic) mirror descent method, in order to significantly reduce the cost per iteration of the latter algorithm. We establish the rate of convergence of the SBMD method along with its associated large-deviation results for solving general nonsmooth and stochastic optimization problems. We also introduce variants of this method and establish their rate of convergence for solving strongly convex, smooth, and composite optimization problems, as well as certain nonconvex optimization problems. To the best of our knowledge, all these developments related to the SBMD methods are new in the stochastic optimization literature. Moreover, some of our results seem to be new for block coordinate descent methods for deterministic optimization.

109 citations

Journal ArticleDOI
TL;DR: This strategy builds upon a combination of techniques from two-stage stochastic programming and level-set-based shape optimization and usage of linear elasticity and quadratic objective functions to obtain a computational cost which scales linearly in the number of linearly independent applied forces.
Abstract: We present an algorithm for shape optimization under stochastic loading and representative numerical results. Our strategy builds upon a combination of techniques from two-stage stochastic programming and level-set-based shape optimization. In particular, usage of linear elasticity and quadratic objective functions permits us to obtain a computational cost which scales linearly in the number of linearly independent applied forces, which often is much smaller than the number of different realizations of the stochastic forces. Numerical computations are performed using a level set method with composite finite elements both in two and in three spatial dimensions.

109 citations

Book
21 Mar 2016
TL;DR: A tutorial on partially observable markov decision processes, a tutorial on controlled stochastic process encyclopedia of mathematics, and optimal control of partially observable piecewise.
Abstract: Covering formulation, algorithms, and structural results, and linking theory to real-world applications in controlled sensing (including social learning, adaptive radars and sequential detection), this book focuses on the conceptual foundations of partially observed Markov decision processes (POMDPs). It emphasizes structural results in stochastic dynamic programming, enabling graduate students and researchers in engineering, operations research, and economics to understand the underlying unifying themes without getting weighed down by mathematical technicalities. Bringing together research from across the literature, the book provides an introduction to nonlinear filtering followed by a systematic development of stochastic dynamic programming, lattice programming and reinforcement learning for POMDPs. Questions addressed in the book include: when does a POMDP have a threshold optimal policy? When are myopic policies optimal? How do local and global decision makers interact in adaptive decision making in multi-agent social learning where there is herding and data incest? And how can sophisticated radars and sensors adapt their sensing in real time?

109 citations

Journal ArticleDOI
TL;DR: The derivations of mean and variance–covariance of the stochastic passenger flows and dis-utility terms involved in the route/mode choice model under the common-line framework are provided.
Abstract: This paper proposes a multi-modal transport network assignment model considering uncertainties in both demand and supply sides of the network. These uncertainties are due to adverse weather conditions with different degrees of impacts on different modes. The paper provides the derivations of mean and variance–covariance of the stochastic passenger flows and dis-utility terms involved in the route/mode choice model under the common-line framework. The risk-averse travelers are assumed to consider both the mean and variance of the random perceived travel time on each multi-modal path in their path choice decisions. The model also considers travelers’ perception errors by using a Probit stochastic user equilibrium framework which is formulated as fixed point problem. A heuristic solution algorithm is proposed to solve the fixed point problem. Numerical examples are presented to illustrate the applications of the proposed model.

108 citations

Journal ArticleDOI
TL;DR: A sequential sampling procedure for a class of stochastic programs that estimates the optimality gap of a candidate solution from a sequence of feasible solutions generated by solving a series of sampling problems with increasing sample size.
Abstract: We develop a sequential sampling procedure for a class of stochastic programs. We assume that a sequence of feasible solutions with an optimal limit point is given as input to our procedure. Such a sequence can be generated by solving a series of sampling problems with increasing sample size, or it can be found by any other viable method. Our procedure estimates the optimality gap of a candidate solution from this sequence. If the point estimate of the optimality gap is sufficiently small according to our termination criterion, then we stop. Otherwise, we repeat with the next candidate solution from the sequence under an increased sample size. We provide conditions under which this procedure (i) terminates with probability one and (ii) terminates with a solution that has a small optimality gap with a prespecified probability.

108 citations


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