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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.


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Book
08 Dec 2010
TL;DR: Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems that are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns.
Abstract: Solving optimization problems in complex systems often requires the implementation of advanced mathematical techniques. Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. QP problems arise in fields as diverse as electrical engineering, agricultural planning, and optics. Given its broad applicability, a comprehensive understanding of quadratic programming is a valuable resource in nearly every scientific field. Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems. The presentation focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming. The reader is required to have a basic knowledge of calculus in several variables and linear algebra.

182 citations

Journal ArticleDOI
TL;DR: This paper discusses alternative decomposition methods in which the second-stage integer subproblems are solved using branch-and-cut methods, and lays the foundation for two-stage stochastic mixed-integer programs.
Abstract: Decomposition has proved to be one of the more effective tools for the solution of large-scale problems, especially those arising in stochastic programming. A decomposition method with wide applicability is Benders' decomposition, which has been applied to both stochastic programming as well as integer programming problems. However, this method of decomposition relies on convexity of the value function of linear programming subproblems. This paper is devoted to a class of problems in which the second-stage subproblem(s) may impose integer restrictions on some variables. The value function of such integer subproblem(s) is not convex, and new approaches must be designed. In this paper, we discuss alternative decomposition methods in which the second-stage integer subproblems are solved using branch-and-cut methods. One of the main advantages of our decomposition scheme is that Stochastic Mixed-Integer Programming (SMIP) problems can be solved by dividing a large problem into smaller MIP subproblems that can be solved in parallel. This paper lays the foundation for such decomposition methods for two-stage stochastic mixed-integer programs.

182 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present the CALM model which has been designed to deal with uncertainty affecting both assets (in either the portfolio or the market) and liabilities (in the form of scenario dependent payments or borrowing costs).
Abstract: Multistage stochastic programming (in contrast to stochastic control) has found wide application in the formulation and solution of financial problems characterized by a large number of state variables and a generally low number of possible decision stages. The literature on the use of multistage recourse modelling to formalize complex portfolio optimization problems dates back to the early seventies, when the technique was first adopted to solve a fixed interest security portfolio problem. We present here the CALM model which has been designed to deal with uncertainty affecting both assets (in either the portfolio or the market) and liabilities (in the form of scenario dependent payments or borrowing costs). We consider as an instance a pension fund problem in which portfolio rebalancing is allowed over a long-term horizon at discrete time points and where liabilities refer to five different classes of pension contracts. The portfolio manager, given an initial wealth, seeks the maximization of terminal wealth at the horizon, with investment returns modelled as discrete state random vectors. Decision vectors represent possible investments in the market and holding or selling assets in the portfolio, as well as borrowing decisions from a credit line or deposits with a bank. Computational results are presented for a set of 10-stage portfolio problems using different solution methods and libraries (OSL,CPLEX,OB1). The portfolio problem with an underlying vector data process which allows up to 2688 realizations at the 10 year horizon is solved on an IBM RS6000/590 for a set of twenty four large scale test problems using the simplex and barrier methods provided by CPLEX (the latter for either linear or quadratic objective), the predictor/corrector interior point method provided in OB1, the simplex method of OSL, the MSLiP-OSL code instantiating nested Benders decomposition with subproblem solution using OSL simplex and the current version of MSLiP.

181 citations

Journal ArticleDOI
TL;DR: Algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform are described and large sample-average approximations of problems from the literature are presented.
Abstract: We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region method. The parallel platform of choice is the dynamic, heterogeneous, opportunistic platform provided by the Condor system. The algorithms are of master-worker type (with the workers being used to solve second-stage problems), and the MW runtime support library (which supports master-worker computations) is key to the implementation. Computational results are presented on large sample-average approximations of problems from the literature.

181 citations

Journal ArticleDOI
TL;DR: This work considers the case when customers can call in orders during the daily operations, and a heuristic solution method is developed where sample scenarios are generated, solved heuristically and combined iteratively to form a solution to the overall problem.
Abstract: The statement of the standard vehicle routing problem cannot always capture all aspects of real-world applications. As a result, extensions or modifications to the model are warranted. Here we consider the case when customers can call in orders during the daily operations; i.e., both customer locations and demands may be unknown in advance. This is modeled as a combined dynamic and stochastic programming problem, and a heuristic solution method is developed where sample scenarios are generated, solved heuristically, and combined iteratively to form a solution to the overall problem.

180 citations


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