A Persistency Model and Its Applications in Choice Modeling

Given a discrete optimization problem $Z(\mb{\tilde{c}})=\max\{\mb{\tilde{c}}’\mb{x}:\mb{x}\in \mathcal{X}\}$, with objective coefficients $\mb{\tilde{c}}$ chosen randomly from a distribution ${\mathcal{\theta}}$, we would like to evaluate the expected value $E_\theta(Z(\mb{\tilde{c}}))$ and the probability $P_{\mathcal{\theta}}(x^*_i(\mb{\tilde{c}})=k)$ where $x^*(\mb{\tilde{c}})$ is an optimal solution to $Z(\mb{\tilde{c}})$. We call this the persistency problem for a discrete optimization problem under uncertain objective, and $P_{\mathcal{\theta}}(x^*_i(\mb{\tilde{c}})=k)$, the … Read more

Pricing A Class of Multiasset Options using Information on Smaller Subsets of Assets

In this paper, we study the pricing problem for the class of multiasset European options with piecewise linear convex payoff in the asset prices. We derive a simple upper bound on the price of this option by constructing a static super-replicating portfolio using cash and options on smaller subsets of assets. The best upper bound … Read more

MINLP Strengthening for Separable Convex Quadratic Transportation-Cost UFL

In the context of a variation of the standard UFL (Uncapacitated Facility Location) problem, but with an objective function that is a separable convex quadratic function of the transportation costs, we present some techniques for improving relaxations of MINLP formulations. We use a disaggregation principle and a strategy of developing model-specific valid inequalities (some nonlinear), … Read more

A Short Note on the Probabilistic Set Covering Problem

In this paper we address the following probabilistic version (PSC) of the set covering problem: min { cx | P (Ax>= xi) >= p, x_{j} in {0,1} j in N} where A is a 0-1 matrix, xi is a random 0-1 vector and p in (0,1] is the threshold probability level. In a recent development … Read more

Recruiting Suppliers for Reverse Production Systems: an MDP Heuristics Approach

In order to achieve stable and sustainable systems for recycling post-consumer goods, frequently it is necessary to concentrate the flows from many collection points of suppliers to meet the volume requirements for the recycler. The collection network must be grown over time to maximize the collection volume while keeping costs as low as possible. This … Read more

Covering models with time-dependent demand

In this paper a covering model for locating facilities with time-dependent demand is introduced. Not only the facility locations, but also the instants at which such facilities become operative, are considered as decision variables in order to determine the maximal-profit decision. Expressed as a mixed nonlinear integer program, structural properties are derived for particular demand … Read more

LIBOPT – An environment for testing solvers on heterogeneous collections of problems

The Libopt environment is both a methodology and a set of tools that can be used for testing, comparing, and profiling solvers on problems belonging to various collections. These collections can be heterogeneous in the sense that their problems can have common features that differ from one collection to the other. Libopt brings a unified … Read more

On large scale unconstrained optimization problems and higher order methods

Third order methods will in most cases use fewer iterations than a second order method to reach the same accuracy. However, the number of arithmetic operations per iteration is higher for third order methods than a second order method. Newton’s method is the most commonly used second order method and Halley’s method is the most … Read more

Using exact penalties to derive a new equation reformulation of KKT systems associated to variational inequalities

In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We … Read more

On the Global Solution of Linear Programs with Linear Complementarity Constraints

This paper presents a parameter-free integer-programming based algorithm for the global resolution of a linear program with linear complementarity constraints (LPEC). The cornerstone of the algorithm is a minimax integer program formulation that characterizes and provides certificates for the three outcomes—infeasibility, unboundedness, or solvability—of an LPEC. An extreme point/ray generation scheme in the spirit of … Read more