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Dual algorithms based on the proximal bundle method for solving convex minimax fractional programs. (English) Zbl 1438.90347

Summary: In this work, we propose an approximating scheme based on the proximal point algorithm, for solving generalized fractional programs (GFP) by their continuous reformulation, also known to as partial dual counterparts of GFP. Bundle dual algorithms are then derived from this scheme. We prove the convergence and the rate of convergence of these algorithms. As for dual algorithms, the proposed methods generate a sequence of values that converges from below to the minimal value of \((P)\), and a sequence of approximate solutions that converges to a solution of the dual problem. For certain classes of problems, the convergence is at least linear.

MSC:

90C32 Fractional programming
90C25 Convex programming
49K35 Optimality conditions for minimax problems
49M29 Numerical methods involving duality
49M37 Numerical methods based on nonlinear programming
90C20 Quadratic programming
90C47 Minimax problems in mathematical programming
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