A Three-Phase Algorithm for Semi-Infinite Programs

In this paper we define general classes of nonlinear semi-infinite programs and developea unified computational scheme for their numerical treatment. This scheme is based on the fact that necessary optimality conditions may he expressed in the form of a nonlinear system of equations with finitely many equations and unknowns. The computational treatment proceeds in three phases: i) A discretized version of the given task is solved, giving an approximate solution;ii) A nonlinear system defining optimality conditions is derived;iii) This system is solved numerically. In general, the structure of the nonlinear system is not known before completion of Phase i). Several applications are indicated.

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