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ε-Optimal solutions in nondifferentiable convex programming and some related questions

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In this paper we present ε-optimality conditions of the Kuhn-Tucker type for points which are within ε of being optimal to the problem of minimizing a nondifferentiable convex objective function subject to nondifferentiable convex inequality constraints, linear equality constraints and abstract constraints. Such ε-optimality conditions are of interest for theoretical consideration as well as from the computational point of view. Some illustrative applications are made. Thus we derive an expression for the ε-subdifferential of a general convex ‘max function’. We also show how the ε-optimality conditions given in this paper can be mechanized into a bundle algorithm for solving nondifferentiable convex programming problems with linear inequality constraints.

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Research sponsored by W.T.O.C.D. CA79-356 and 79-360.

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Strodiot, J.J., Nguyen, V.H. & Heukemes, N. ε-Optimal solutions in nondifferentiable convex programming and some related questions. Mathematical Programming 25, 307–328 (1983).

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