We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose a new portfolio optimization model involving stochastic dominance constraints on the portfolio return. We develop optimality and duality theory for these models. We construct equivalent optimization models with utility functions. Numerical illustration … Read more
We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk functions. Citation Preprint Article Download View Optimization of Convex Risk Functions
The goal of this paper is to formulate and solve structural optimization problems with constraints on the global stability of the structure. The stability constraint is based on the linear buckling phenomenon. We formulate the problem as a nonconvex semidefinite programming problem and introduce an algorithm based on the Augmented Lagrangian method combined with the … Read more
This paper addresses the one-machine scheduling problem where the objective is to minimize a sum of costs such as earliness-tardiness costs. Since the sequencing problem is NP-hard, local search is very useful for finding good solutions. Unlike scheduling problems with regular cost functions, the scheduling (or timing) problem is not trivial when the sequence is … Read more
The one-machine scheduling problem with sequence-dependent setup times and costs and earliness-tardiness penalties is addressed. This problem is NP-complete, so that local search approaches are very useful to efficiently find good feasible schedules. In this paper, we present an extension of the dynasearch neighborhood for this problem. Finding the best schedule in this neighborhood is … Read more
In the recently published book on the Traveling Salesman Problem, half of Chapter 6 is devoted to domination analysis (DA) of heuristics for the Traveling Salesman Problem. Another chapter (in preparation) is a detailed overview of the whole area of DA. Both chapters are of considerable length. The purpose of this paper is to give … Read more
There are numerous algebraic modeling languages for generating linear programs and numerous solvers for computing solutions to linear programs. This proliferation of modeling languages and solvers is frustrating to modelers who find that only certain languages connect to certain solvers. One way to encourage modeler-solver compatibility is to use a standard representation of a problem … Read more
We describe strong mixed-integer programming formulations for robust mixed 0-1 programming with uncertainty in the objective coefficients. In particular, we focus on an objective uncertainty set described as a polytope with a budget constraint. We show that for a robust 0-1 problem, there is a tight linear programming formulation with size polynomial in the size … Read more
Interior-point methods (IPMs), originally conceived in the context of linear programming have found a variety of applications in integer programming, and combinatorial optimization. This survey presents an up to date account of IPMs in solving NP-hard combinatorial optimization problems to optimality, and also in developing approximation algorithms for some of them. The surveyed approaches include … Read more
This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (l,S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (l,S) inequalities to a general class of valid inequalities, called the (Q,S_Q) inequalities, and we … Read more