»ã±¨±êÌâ (Title)£ºGlobal optimization algorithms for fractional programming problems £¨·Öʽ¹æ»®ÎÊÌâµÄÈ«¾ÖÓÅ»¯Ëã·¨£©

»ã±¨ÈË (Speaker)£ºÉêÅàƼ ½ÌÊÚ£¨»ª±±Ë®ÀûË®µç´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê5ÔÂ29ÈÕ (ÖÜÈý) 10:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÐì×Ë ½ÌÊÚ

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»ã±¨ÌáÒª£ºFractional programming problems have been widely studied due to their importance from both theoretical and practical perspectives. Theoretically, fractional programming problem has many locally optimal solutions which are not globally optimal. In practice, it has spawned a wide variety of applications in bond portfolio optimization, system reliability analysis, computer vision and so on. From the computational point of view, various approaches have been proposed to tackle it, such as outer approximation algorithm, branch and bound algorithm, approximation algorithm and so on. In this talk, we focus on two types of fractional programming problems: the sum of linear ratios programming problem and the minimax linear fractional programming problem. For sum of linear ratios problem, a spatial branch-and-bound algorithm is proposed by utilizing a second-order cone relaxation technique. This algorithm incorporates a region compression technique and an adaptive branching rule to enhance convergence. We also introduce a branch-and-bound algorithm based on the relaxation of a box-constrained two-layer problem. Additionally, the one-dimensional branching rule based branch-and-bound algorithm is considered for minimax linear fractional programming. Finally, the convergence and complexity of the developed algorithms are analyzed.