Tightening simple mixed-integer sets with guaranteed bounds
We extend work on generating relaxations of simple sets with guaranteed bounds. CitationUnpublished. Columbia University, July 2008.ArticleDownload View PDF
Month: July 2008
Asymmetry and Ambiguity in Newsvendor Models
The traditional decision-making framework for newsvendor models is to assume a distribution of the underlying demand. However, the resulting optimal policy is typically sensitive to the choice of the distribution. A more conservative approach is to assume that the distribution belongs to a set parameterized by a few known moments. An ambiguity-averse newsvendor would choose … Read more
Representation of nonnegative convex polynomials
We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic set $K$ of $R^n$. Namely, they belong to a specific subset of the quadratic module generated by the concave polynomials that define $K$. CitationTo appear in Archiv der MathematikArticleDownload View PDF
A New Full-Newton step (n)$ Infeasible Interior-Point Algorithm for Semidefinite Optimization
Interior-point methods for semidefinite optimization have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, the second author designed an efficient primal-dual infeasible interior-point algorithm with full Newton steps for linear optimization problems. In this paper we extend the algorithm to semidefinite optimization. The algorithm constructs strictly feasible iterates for a sequence … Read more
GRASP: Basic components and enhancements
GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinatorial optimization problems. Each GRASP iteration is usually made up of a construction phase, where a feasible solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution … Read more
Hybrid GRASP heuristics
Experience has shown that a crafted combination of concepts of different metaheuristics can result in robust combinatorial optimization schemes and produce higher solution quality than the individual metaheuristics themselves, especially when solving difficult real-world combinatorial optimization problems. This chapter gives an overview of different ways to hybridize GRASP (Greedy Randomized Adaptive Search Procedures) to create … Read more
GRASP
GRASP is a multi-start metaheuristic for combinatorial optimization problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. An intensification … Read more
GRASP: Advances and applications
GRASP is a multi-start metaheuristic for combinatorial optimization problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this … Read more
Extended Formulations for Packing and Partitioning Orbitopes
We give compact extended formulations for the packing and partitioning orbitopes (with respect to the full symmetric group) described and analyzed in Kaibel and Pfetsch (Math. Program. 114 (1), 2008, 1-36). These polytopes are the convex hulls of all 0/1-matrices with lexicographically sorted columns and at most, resp. exactly, one 1-entry per row. They are … Read more
Semi-infinite programming, duality, discretization and optimality conditions
The aim of this paper is to give a survey of some basic theory of semi-infinite programming. In particular, we discuss various approaches to derivations of duality, discretization and first and second order optimality conditions. Some of the surveyed results are well known while others seem to be less noticed in that area of research. … Read more