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Abstract: In this paper, we first weaken some assumptions in Jiao et al. (2005) [9] and discuss the continuity and the directional differentiability of the objective function. Furthermore, we investigate the optimality conditions for unconstrained and constrained generalized minimax programming. These optimality conditions are mixed ones that include different conditions at different directions, which is suitable for the non-differentiable objective function. For constrained problem we exploit two kinds of analysis methods to obtain some different optimality conditions. Moreover, we show these optimality conditions by some examples. [Copyright &y& Elsevier]

Abstract: A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems. [Copyright &y& Elsevier]