Approximation procedures based on the method of multipliers

In this paper, we consider a method for solving certain optimization problems with constraints, nondifferentiabilities, and other ill-conditioning terms in the cost functional by approximating them by well-behaved optimization problems. The approach is based on methods of multipliers. The convergence properties of the methods proposed can be inferred from corresponding properties of multiplier methods with partial elimination of constraints. A related analysis is provided in this paper.This work was supported in part by the Joint Services Electronics Program (US Army, US Navy, and US Air Force) under Contract No. DAAB-07-72-C-0259, and by the National Science Foundation under Grant No. ENG-74-19332.