Accession Number : ADA193032

Title :   Numerical Optimization.

Descriptive Note : Periodic repts. 1-4, Jul 86-Jan 88,

Corporate Author : ROME UNIV (ITALY) DEPT OF MATHEMATICS

Personal Author(s) : Zirilli, Francesco

PDF Url : ADA193032

Report Date : Jan 1988

Pagination or Media Count : 82

Abstract : The first objective the authors pursued was to build some test problems in the area of linear and nonlinear complementarity problems in order to be able to verify the practical value of our algorithms before submitting them to a detailed mathematical analysis. A large variety of problems of different difficulty belongs to the area of linear and nonlinear complementarity; to start our investigation we have considered three problems that come from the discretization of variational inequalities of mathematical physics. The first two problems are linear complementarity problems; the third one is a nonlinear complementarity problem. The corresponding continuous problems involve ordinary or partial differential operators so that when discretized a large number (up to a few thousand) independent variables can be considered. For these problems existence and uniqueness of the solution can be proved; moreover, they have some intrinsic interest given their mathematical physics interpretation. A FORTRAN computer code implementing these three complementarity problems has been written. The complementarity problems considered above have been translated into a system of nonlinear equations. On the resulting systems of nonlinear equations the algorithm DAFNE based on the use of ordinary differential equations and the algorithm SIGMA based on the use of stochastic differential equations have been used.

Descriptors :   *ALGORITHMS, *OPTIMIZATION, DIFFERENTIAL EQUATIONS, FORTRAN, INEQUALITIES, MACHINE CODING, MATHEMATICAL ANALYSIS, MATHEMATICS, NONLINEAR ALGEBRAIC EQUATIONS, NUMERICAL METHODS AND PROCEDURES, OPERATORS(MATHEMATICS), PARTIAL DIFFERENTIAL EQUATIONS, PHYSICS, STOCHASTIC PROCESSES

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE