Inverse optimization perturbs objective function to make an initial feasible solution optimal with respect to perturbed objective function while minimizing cost of perturbation. We extend inverse optimization to two-stage stochastic linear programs. Since the resulting model grows with number of scenarios, we present two decomposition approaches for solving these problems. CitationUnpublished: 07-1, University of Pittsburgh, … Read more
This paper provides sufficient conditions for the optimal value function of a given linear semi-infinite programming problem to depend linearly on the size of the perturbations, when these perturbations are directional, involve either the cost coefficients or the right-hand-side function or both, and they are sufficiently small. Two kinds of partitions are considered. The first … Read more
When is the linear image of a closed convex cone closed? We present very simple, and intuitive necessary conditions, which 1) unify, and generalize seemingly disparate, classical sufficient conditions: polyhedrality of the cone, and “Slater” type conditions; 2) are necessary and sufficient, when the dual cone belongs to a class, that we call nice cones. … Read more
Algebraic modelling languages have gained wide acceptance and use in Mathematical Programming by researchers and practitioners. At a basic level, stochastic programming models can be defined using these languages by constructing their deterministic equivalent. Unfortunately, this leads to very large model data instances. We propose a direct approach in which the random values of the … Read more
The robust portfolio selection problems have recently been studied by several researchers (e.g., see \cite{GoIy03,ErGoIy04,HaTu04,TuKo04}). In their work, the “separable” uncertainty sets of the problem parameters (e.g., mean and covariance of the random returns) were considered. These uncertainty sets share two common drawbacks: i) the actual confidence level of the uncertainty set is unknown, and … Read more
In this paper we explore properties of a family of probability density functions, called norm-induced densities, defined as $$f_t(x) = \left\{ \begin{array}{ll} \displaystyle \frac{ e^{-t\|x\|^p}dx}{\int_K e^{-t\|y\|^p}dy}, & x \in K \\ 0, & x \notin K,\\ \end{array}\right. $$ where $K$ is a $n$-dimensional convex set that contains the origin, parameters $t > 0$ and $p … Read more
A new initialization or `Phase I’ strategy for feasible interior point methods for linear programming is proposed that computes a point on the primal-dual central path associated with the linear program. Provided there exist primal-dual strictly feasible points — an all-pervasive assumption in interior point method theory that implies the existence of the central path … Read more
Every multistage stochastic programming problem with recourse (MSPR) contains a filtration process. In this research, we created a notation that makes the filtration process the central syntactic construction of the MSPR. As a result, we achieve lower redundancy and higher modularity than is possible with the mathematical notation commonly associated with stochastic programming. To experiment … Read more
The NEOS Server provides access to a variety of optimization resources via the Internet. The new Kestrel interface to the Server enables local modeling environments to request NEOS optimization services and retrieve the results for local visualization and analysis, so that users have the same convenient access to remote NEOS solvers as to those installed … Read more
In this paper we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove … Read more