Solving Nonlinear Portfolio Optimization Problems with the Primal-Dual Interior Point Method

Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios per time stage. So far models treated by mathematical programming approaches have been limited to simple linear … Read more

A Parallel Primal-Dual Interior-Point Method for Semidefinite Programs Using Positive Definite Matrix Completion

A parallel computational method SDPARA-C is presented for SDPs (semidefinite programs). It combines two methods SDPARA and SDPA-C proposed by the authors who developed a software package SDPA. SDPARA is a parallel implementation of SDPA and it features parallel computation of the elements of the Schur complement equation system and a parallel Cholesky factorization of … Read more

Parallel Strategies for GRASP with path-relinking

A Greedy Randomized Adaptive Search Procedure (GRASP) is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and local search. Path-relinking is an intensification strategy that explores trajectories that connect high quality solutions. We analyze two parallel strategies for GRASP with path-relinking and propose a criterion … Read more

A methodology for the analysis of parallel GRASP strategies

In this paper, we describe a methodology for the analysis of greedy randomized adaptive search procedures (GRASP). GRASP is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and a local search. Hybrid approaches of GRASP with path-relinking developed for the 3-index assignment problem (AP3) and … Read more

SDPARA : SemiDefinite Programming Algorithm PARAllel Version

Abstract: The SDPA (SemiDefinite Programming Algorithm) is known as efficient computer software based on primal-dual interior-point method for solving SDPs (Semidefinite Programs). In many applications, however, some SDPs become larger and larger, too large for the SDPA to solve on a single processor. In execution of the SDPA applied to large scale SDPs, the computation … Read more

Pattern Search Methods for User-Provided Points:Application to Molecular Geometry Problems

This paper deals with the application of pattern search methods to the numerical solution of a class of molecular geometry problems with important applications in molecular physics and chemistry. The goal is to find a configuration of a cluster or a molecule with minimum total energy. The minimization problems in this class of geometry molecular … Read more

Parallel Computing on Semidefinite Programs

This paper demonstrates how interior-point methods can use multiple processors efficiently to solve large semidefinite programs that arise in VLSI design, control theory, and graph coloring. Previous implementations of these methods have been restricted to a single processor. By computing and solving the Schur complement matrix in parallel, multiple processors enable the faster solution of … Read more

GRASP with path relinking for the three-index assignment problem

This paper describes variants of GRASP (greedy randomized adaptive search procedure) with path relinking for the three index assignment problem (AP3). GRASP is a multi-start metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and of a local search. Path relinking is an intensification strategy that explores … Read more

Optimization on Computational Grids

We define the concept of a computational grid, and describe recent work in solving large and complex optimization problems on this type of platform; in particular, integer programming, the quadratic assignment problem, and stochastic programming problems. This article focuses on work conducted in the metaneos project. Citation Preprint, Mathematics and Computer Science Division, Argonne National … Read more

A Parallel, Linear Programming Based Heuristic for Large Scale Set Partitioning Problems

We describe a parallel, linear programming and implication based heuristic for solving set partitioning problems on distributed memory computer architectures. Our implementation is carefully designed to exploit parallelism to greatest advantage in advanced techniques like preprocessing and probing, primal heuristics, and cut generation. A primal-dual subproblem simplex method is used for solving the linear programming … Read more