关键词: 分式优化, 鲁棒最优性, 鲁棒对偶性

Abstract:

Fractional optimization with sum of squares convex-concave polynomials is often involved in the uncertain data processing. This paper is concerned with its robust optimal solutions. We first give optimality conditions of robust optimal solutions for the uncertain fractional polynomial optimization problem in terms of robust optimization and a normal cone constraint qualification condition. Then, we give a robust dual problem to this uncertain fractional polynomial optimization problem and establish robust weak and strong duality properties between them. Moreover, we obtain exact sum of squares relaxation results for this uncertain fractional polynomial optimization problem.

Key words: fractional optimization, robust optimality, robust duality