A Subgradient Algorithm for Certain Minimax and Minisum Problems.
FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
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This paper presents a subgradient algorithm for the problem Min Fx x an element of R to the n power where Fx Max f sub ix i 1, 2, ..., m and where f sub ix sum over j of f sub ijx. Each f sub ij is assumed to be a proper convex function, and the number of different subgradient sets associated with nondifferentiable points of f sub ij is assumed to be finite on any bounded set. Problems belonging to this class include those where the f sub ij are l sub p - norms 1 or p or infinity for example, the linear approximation problem and both the minimax and minisum problems of location theory. Convergence of the algorithm to an epsilon - optimal solution is proved and its effectiveness demonstrated by solving a number of problems from location theory and linear approximation theory. Our computational results are compared with other solution methods.
- Theoretical Mathematics