Document Type

Technical Report

Publication Date

Winter 2-1-1980

Abstract

We present a new class of algorithms for determining whether there exists a point x ɛ Rn satisfying the nonlinear inequality constraints ci(x) ≤ 0, i=1, …, m, subject perhaps to satisfying linear inequality constraints lj¬(x) ≤0, j=1, …,k which are known to be feasible. Our algorithm consists of solving a sequence of linearly constrained optimization problems, using a sequence of objective functions ф(x,p) which are at least twice continuously differentiable, and which are generated by monotonically increasing the value of the non-negative parameter p. It is shown that in almost all cases, once p reaches or exceeds some finite value, that the solution to the linearily constrained optimization problem either is a feasible point, or establishes the infeasibility of the set of constraints. Computational results are presented in which the algorithm performs satisfactorily on feasible and on infeasible systems.

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