A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version … Read more
This paper presents an algorithmic extension of Powell’s UOBYQA algorithm (”Unconstrained Optimization BY Quadratical Approximation”). We start by summarizing the original algorithm of Powell and by presenting it in a more comprehensible form. Thereafter, we report comparative numerical results between UOBYQA, DFO and a parallel, constrained extension of UOBYQA that will be called in the … Read more
We describe version 3.0 of the COPS set of nonlinearly constrained optimization problems. We have added new problems, as well as streamlined and improved most of the problems. We also provide a comparison of the FILTER, KNITRO, LOQO, MINOS, and SNOPT solvers on these problems. Citation Technical Report ANL/MCS-TM-273, Argonne National Laboratory, 02/04. Article Download … Read more
Self-regular based interior point methods present a unified novel approach for solving linear optimization and conic optimization problems. So far it was not known if the new Self-Regular IPMs can lead to similar advances in computational practice as shown in the theoretical analysis. In this paper, we present our experiences in developing the software package … Read more
We describe FORTRAN subroutines for network flow optimization using an interior point network flow algorithm. We provide FORTRAN and C language drivers, as well as C language functions that, together with the subroutines, make up PDNET (Portugal, Resende, Veiga, and Júdice, 2000). The algorithm is described in detail and its implementation is outlined. Usage of … Read more
There are numerous algebraic modeling languages for generating linear programs and numerous solvers for computing solutions to linear programs. This proliferation of modeling languages and solvers is frustrating to modelers who find that only certain languages connect to certain solvers. One way to encourage modeler-solver compatibility is to use a standard representation of a problem … Read more
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