We introduce two-stage stochastic semidefinite programs with recourse and present a Benders decomposition based linearly convergent interior point algorithms to solve them. This extends the results in Zhao [16] wherein it was shown that the logarithmic barrier associated with the recourse function of two-stage stochastic linear programs with recourse behaves as a strongly self-concordant barrie...

This paper addresses two major issues related to the convergence of generalized Benders decomposition which is an algorithm for the solution of mixed integer linear and nonlinear programming problems. First, it is proved that a mixed integer nonlinear programming formulation with zero nonlinear programming relaxation gap requires only one Benders cut in order to converge, namely the cut corresp...

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the al...

In this paper, we derive (partial) convex hull for deterministic multi-constraint polyhedral conic mixed integer sets with multiple variables using rounding (CMIR) cut-generation procedure of Atamtürk and Narayanan (Math Prog 122:1–20, 2008), thereby extending their result a simple set single constraint one variable. We then introduce two-stage stochastic p-order programs (denoted by TSS-CMIPs)...

the hub location decision is a long term investment and any changes in it take considerable time and money. in real situations, some parameters are uncertain hence, deterministic models cannot be more efficient. the ability of two-stage stochastic programming is to make a long-term decision by considering effects of it in short term decisions simultaneously. in the two-stage stochastic programm...

We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to select the most relevant Benders cuts. We propose a limited memory variant of Level 1 and show the convergence of DDP combined with the Territory algorithm,...

Network design problems arise in many different application areas such as air freight, highway traffic and communications systems. This thesis concerns the development, analysis and testing of new techniques for solving network design problems. We study the application of Benders decomposition to solve mixed integer programming formulations of the network design problem. A new methodology for a...

is eventually found and the method terminates. As convergence may require a large amount of computing time for hard instances, the method unsatisfactory from a heuristic point of view. Proximity Search is a recently-proposed heuristic paradigm in which the problem at hand is modified and iteratively solved with the aim of producing a sequence of improving feasible solutions. As such, Proximity ...

Logic-based Benders decomposition (LBBD) has improved the state of the art for solving a variety of planning and scheduling problems, in part by combining the complementary strengths of constraint programming (CP) and mixed integer programming (MIP). We undertake a computational analysis of specific factors that contribute to the success of LBBD, to provide guidance for future implementations. ...