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Global convergence of a semi-infinite optimization method

A new algorithm for minimizing locally Lipschitz functions using approximate function values is presented. It yields a method for minimizing semi-infinite exact penalty functions that parallels the trust region methods used in composite nondifferentiable optimization. A finite method for approximating a semi-infinite exact penalty function is developed. A uniform implicit function theorem is established during this development. An implementation and test results for the approximate penalty function are included.

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