In the context of SQP methods or, more recently, of sequential semidefinite programming methods, it is common practice to construct a positive semidefinite approximation of the Hessian of the Lagrangian. The Hessian of the augmented Lagrangian is a suitable approximation as it maintains local superlinear convergence under appropriate assumptions. In this note we give a … Read more
This paper draws from our experience in developing the AMPL modeling language, to show where numerical issues have been crucial to modeling language design and where modeling language advances have strongly influenced the design of solvers. Citation Proceedings of the 20th Biennial Conference on Numerical Analysis, Dundee, Scotland, D.F. Griffiths and G.A. Watson, eds., University … Read more
Citation Research report, PCS Inc., Halifax, NS, Canada; November 2003. Submitted for publication. Article Download View GAMS/LGO Nonlinear Solver Suite: Key Features, Usage, and Numerical Performance
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
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
This work introduces a distributed branch-and-bound algorithm to be run on computational Grids. Grids are often organized in a hierarchical fashion: clusters of processors connected via high-speed links, while the clusters themselves are geographically distant and connected through slower links. Our algorithm does not employ the usual master-worker paradigm and it considers the hierarchical structure … Read more
The nearest \cm\ problem is to find a positive semidefinite matrix with unit diagonal that is nearest in the Frobenius norm to a given symmetric matrix $A$. This problem can be formulated as an optimization problem with a quadratic objective function and semidefinite programming constraints. Using such a formulation, we derive and test a primal-dual … Read more
Issues of implementation of a library for parallel interior-point methods for quadratic programming are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modeled. The efficiency of the solver is … Read more
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
As part of Performance World, we describe an automation server (PAVER: http://www.gamsworld.org/performance/paver) to help facilitate reproducible performance analysis of benchmarking data for optimization software. Although PAVER does not solve optimization problems, it automates the task of performance data analysis and visualization, taking into account various performance metrics. These include not only robustness and efficiency, but … Read more