Constrained optimization applying decomposed unlimited point method based on KKT condition

Constrained optimization problems play a significant role within optimization problems. In this paper, a novel method, decomposed unlimited point method (DUPM), is proposed to modify the Karush-Kuhn-Tucker (KKT) condition of constrained optimization problems. In the DUPM, KKT condition can be transformed into equations without any limitation in the variable space. Afterwards, the equivalent equations are solved by Levenberg-Marquardt method (LMM), which is the first attempt ever of applying LMM to such situations. Simulation results on various numerical examples demonstrate that DUPM is able to transform the primal KKT condition into equations without changing the functions' characteristics such as continuity and smoothness unlike nonlinear complementarity problem method (NCPM), and LMM can be widely used to solve the equivalent equations with a quadratic convergence rate.