## A Log-Barrier Method With Benders Decomposition For Solving Two-Stage Stochastic Programs (1999)

Venue: | Mathematical Programming 90 |

Citations: | 15 - 6 self |

### BibTeX

@TECHREPORT{Zhao99alog-barrier,

author = {Gongyun Zhao},

title = {A Log-Barrier Method With Benders Decomposition For Solving Two-Stage Stochastic Programs},

institution = {Mathematical Programming 90},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. When applied to problems with a finite number of scenarios, the algorithm is shown to converge globally and to run in polynomial-time. Key Words: Stochastic programming, Large-scale linear programming, Barrier function, Interior point methods, Benders decomposition, Complexity. Abbreviated Title: A log-barrier method with Benders decomposition AMS(MOS) subject classifications: 90C15, 90C05, 90C06, 90C60. 1 1. Introduction In this paper we propose an algorithm for solving two-stage stochastic programs, establish fundamental properties of the algorithm, and analyze the convergence. An example of a two-stage stochastic program is a production planning problem. The production and demand take place in the first and second periods, resp...

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Citation Context ...ven higher order methods (see, e.g., [23] [41]) can be used to enhance the convergence. The use of the logarithmic barrier is inspired by the great success of the interior point method. Kojima, et al =-=[22]-=- is the first paper incorporating the interior point method into decomposition. Our method also uses this idea. However, the problem setting and algorithm in this paper are different from those in [22... |

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1 |
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1 |
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