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# Accession Number:

## ADA193032

# Title:

## Numerical Optimization.

# Descriptive Note:

## Periodic repts. 1-4, Jul 86-Jan 88,

# Corporate Author:

## ROME UNIV (ITALY) DEPT OF MATHEMATICS

# Report Date:

## 1988-01-01

# Pagination or Media Count:

##
82.0

# 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.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#