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Parametrizations of Kojima’s system and relations to penalty and barrier functions. (English) Zbl 0871.90086
Summary: We investigate two homotopies that perturb Kojima’s system for describing critical points of a nonlinear optimization problem in finite dimension. Each of them characterizes stationary points of a usual penalty and a new “barrier” function. The latter is a continuous deformation of the objective, symmetric to the penalty from a formal point of view. Stationary points of these functions appear as perturbed critical points and vice versa. This permits new interpretations of the related solution methods and allows estimates of the solutions by using implicit function theorems for Lipschitzian equations.

MSC:
90C30 Nonlinear programming
49M30 Other numerical methods in calculus of variations (MSC2010)
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