Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
Papers published on a yearly basis
Papers
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TL;DR: The case when enough data paths can be generated according to an accepted parametric or nonparametric stochastic model when no assumptions on convexity with respect to the random parameters are required is discussed.
Abstract: A major issue in any application of multistage stochastic programming is the representation of the underlying random data process. We discuss the case when enough data paths can be generated according to an accepted parametric or nonparametric stochastic model. No assumptions on convexity with respect to the random parameters are required. We emphasize the notion of representative scenarios (or a representative scenario tree) relative to the problem being modeled.
493 citations
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TL;DR: This work explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm as well as providing guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients.
489 citations
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01 Jan 2004TL;DR: In this paper, a stochastic dynamic programming (SDP) approach was used to obtain the optimal supervisory control strategy for hybrid vehicles with random Markov processes. But the resulting control strategy was often inherently cycle-beating and lacked a guaranteed level of optimality.
Abstract: The supervisory control strategy of a hybrid vehicle coordinates the operation of vehicle sub-systems to achieve performance targets such as maximizing fuel economy and reducing exhaust emissions. This high-level control problem is commonly referred as the power management problem. In the past, many supervisory control strategies were developed on the basis of a few pre-defined driving cycles, using intuition and heuristics. The resulting control strategy was often inherently cycle-beating and lacked a guaranteed level of optimality. In this study, the power management problem is tackled from a stochastic viewpoint. An infinite-horizon stochastic dynamic optimization problem is formulated. The power demand from the driver is modeled as a random Markov process. The optimal control strategy is then obtained by using stochastic dynamic programming (SDP). The obtained control law is in the form of a stationary full-state feedback and can be directly implemented. Simulation results over standard driving cycles and random driving cycles are presented to demonstrate the effectiveness of the proposed stochastic approach. It was found that the obtained SDP control algorithm outperforms a sub-optimal rule-based control strategy trained from deterministic DP results.
488 citations
01 Jan 2011
482 citations
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TL;DR: A comprehensive study of various mathematical programming methods for structural optimization is presented in this article, where the authors discuss the applicability of modern optimization techniques to structural design problems, and present mathematical programming method from a unified and design engineers' viewpoint.
Abstract: A comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.
482 citations