Algorithms for generating large scale nonlinear programming problems with known degree of difficulty

Abstract

Convex-quadratic functions are defined based on real symmetric positive definite matrices. Gershgorin's Theorem is used for randomly generating positive definite matrices of arbitrary size. A computational algorithm is presented. The concept of degree of difficulty of a test function is introduced and it is used to define an algorithm to generate test problems with varying degree of difficulty. These algorithms when used in conjunction with the Rosen and Suzuki method may be used to generate large scale constrained nonlinear programming problems.