Abstract
In this paper, a feasible descent bundle method for solving inequality constrained Minimax problems is proposed. The main features of the method are: (1) By using the subgradients of functions and the idea of bundle method, it does not assume that the component functions of the original problem are smooth; (2) by adopting the technique of partial cutting-planes model, at each null step, only the function value and subgradient of one component function are needed to generate the new cutting plane, and therefore the computational cost is reduced effectively; (3) it can ensure the feasibility of the serious iterates and the decsent of the objective function; (4) by introducing the technique of subgradient aggregation to aggregate the subgradients in the bundle, the difficulty of numerical calculation and storage is overcome; (5) the algorithm is proved to be globally convergent, and the preliminary numerical results show that the proposed algorithm is effective.
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