Surrogate Constraints Algorithm for Reliability Optimization Problems with Multiple Constraints

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Abstract
This paper presents a surrogate constraints algorithm for solving nonlinear programming, nonlinear integer programming, and nonlinear mixed integer programming problems. The algorithm contains a new technique for generating a succession of vector values of surrogate multiplier (ie, surrogate problems). By using this technique, a computer can keep a polyhedron, which is a vector space of surrogate multipliers to be considered at a certain time, in its memory. Furthermore it can cut the polyhedron by a given hyperplane, and produce the remaining space as the next polyhedron. Simple examples are included.

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