A novel method is presented to analyze the limit for the optimal value of a class of minimax optimization problems with parameter. The minimax optimization problems can be transformed into semi-infinite programming (SIP) problems, and the optimal value series of the SIP problems with parameter are analyzed. First, we obtain that the optimal values of the cost function is monotonically decreasing as the parameter increases, and then the limit exists and can be computed by choosing a sufficiently large parameter. Next, we propose a novel method to obtain the limit of the optimal values by introducing a series of simplified subproblems. We derive the conditions and apply the fixed point theorem to prove that the function obtained by the proposed method is exactly the continuous limit function when the parameter tends to infinity, and the maximum value obtained by the proposed method is exactly the limit of optimal value series as the parameter tends to infinity. For illustration, numerical experiments are demonstrated to show the effectiveness and efficiency of the proposed method.
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