A modified penalty term for the sequential unconstrained minimization technique for convex programming problems

Abstract

The Sequential Unconstrained Minimization Technique (SUMT) for Convex Programming Problems is modified by the introduction of an exponent in the penalty term. The exponent is introduced to increase the rate of convergence of the method for nonlinear problems with solutions on the boundary of one or more constraints. Convergence to the solution of the constrained problem is proved, and it is shown that SUMT is a special case of the general unconstrained function with the exponent equal to one. Results of a sample problem indicate that the rate of convergence is improved and that the computational time for solution is decreased for an exponent less than one.