ASTRAL: An Active Set \inftyhBcTrust-Region Algorithm for Box Constrained Optimization

Categories Bound-constrained Optimization Tags , , ,

An algorithm for solving large-scale nonlinear optimization problems with simple bounds is described. The algorithm is an $\ell_\infty$-norm trust-region method that uses both active set identification techniques as well as limited memory BFGS updating for the Hessian approximation. The trust-region subproblems are solved using primal-dual interior point techniques that exploit the structure of the limited … Read more

Pareto Optima of Multicriteria Integer Linear Programs

Categories Integer Programming, Multi-Criteria Optimization

We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct: 1. polynomial-time algorithms to exactly determine the number of Pareto optima and Pareto strategies; 2. a polynomial-space polynomial-delay prescribed-order enumeration algorithm … Read more

Comments on “Dual Methods for Nonconvex Spectrum Optimization of Multicarrier Systems”

Categories Global Optimization Tags , ,

Yu and Liu’s strong duality theorem under the time-sharing property requires the Slater condition to hold for the considered general nonconvex problem, what is satisfied for the specific application. We further extend the scope of the theorem under Ky Fan convexity which is slightly weaker than Yu&Lui’s time-sharing property. ArticleDownload View PDF

A gradient-based approach for computing Nash equilibria of large sequential games

Categories Convex Optimization, Game Theory, Linear Programming Tags , ,

We propose a new gradient based scheme to approximate Nash equilibria of large sequential two-player, zero-sum games. The algorithm uses modern smoothing techniques for saddle-point problems tailored specifically for the polytopes used in the Nash equilibrium problem. CitationWorking Paper, Tepper School of Business, Carnegie Mellon UniversityArticleDownload View PDF

Facet Defining Inequalities among Graph Invariants: the system GraPHedron

Categories Graphs and Matroids Tags , , ,

We present a new computer system, called GraPHedron, which uses a polyhedral approach to help the user to discover optimal conjectures in graph theory. We define what should be optimal conjectures and propose a formal framework allowing to identify them. Here, graphs with n nodes are viewed as points in the Euclidian space, whose coordinates … Read more

New subroutines for large-scale optimization

Categories Nonlinear Optimization, Optimization Software and Modeling Systems Tags ,

We present fourteen basic FORTRAN subroutines for large-scale unconstrained and box constrained optimization and large-scale systems of nonlinear equations. Subroutines {\tt PLIS} and {\tt PLIP}, intended for dense general optimization problems, are based on limited-memory variable metric methods. Subroutine {\tt PNET}, also intended for dense general optimization problems, is based on an inexact truncated Newton … Read more

Optimization for Simulation: LAD Accelerator

Categories Data-Mining, Optimization of Simulated Systems, Stochastic Approaches Tags , ,

The goal of this paper is to address the problem of evaluating the performance of a system running under unknown values for its stochastic parameters. A new approach called LAD for Simulation, based on simulation and classification software, is presented. It uses a number of simulations with very few replications and records the mean value … Read more

Smooth Optimization Approach for Covariance Selection

Categories Convex and Nonsmooth Optimization, Statistics Tags , ,

In this paper we study a smooth optimization approach for solving a class of non-smooth {\it strongly} concave maximization problems. In particular, we apply Nesterov’s smooth optimization technique \cite{Nest83-1,Nest05-1} to their dual counterparts that are smooth convex problems. It is shown that the resulting approach has $\cO(1/{\sqrt{\epsilon}})$ iteration complexity for finding an $\epsilon$-optimal solution to … Read more

Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems

Categories Applications - Science and Engineering, Bound-constrained Optimization Tags ,

Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared $\ell_2$) error term combined with a sparseness-inducing ($\ell_1$) regularization term.{\it Basis pursuit}, the {\it least absolute shrinkage and selection operator} (LASSO), … Read more