tailieunhanh - báo cáo hóa học: " On ε-optimality conditions for multiobjective fractional optimization problems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: On ε-optimality conditions for multiobjective fractional optimization problems | Kim et al. Fixed Point Theory and Applications 2011 2011 6 http content 2011 1 6 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access On e-optimality conditions for multiobjective fractional optimization problems Moon Hee Kim1 Gwi Soo Kim2 and Gue Myung Lee2 Correspondence gmlee@. kr department of Applied Mathematics Pukyong National University Busan 608-737 Korea Full list of author information is available at the end of the article SpringerOpen0 Abstract A multiobjective fractional optimization problem MFP which consists of more than two fractional objective functions with convex numerator functions and convex denominator functions finitely many convex constraint functions and a geometric constraint set is considered. Using parametric approach we transform the problem MFP into the non-fractional multiobjective convex optimization problem NMCP v with parametric v e Rp and then give the equivalent relation between weakly eefficient solution of MFP and weakly efficient solution of NMCP ĩ. Using the equivalent relations we obtain e-optimality conditions for weakly e-efficient solution for MFP . Furthermore we present examples illustrating the main results of this study. 2000 Mathematics Subject Classification 90C30 90C46. Keywords Weakly E-efficient solution E-optimality condition Multiobjective fractional optimization problem 1 Introduction We need constraint qualifications for example the Slater condition on convex optimization problems to obtain optimality conditions or e-optimality conditions for the problem. To get optimality conditions for an efficient solution of a multiobjective optimization problem we often formulate a corresponding scalar problem. However it is so difficult that such scalar program satisfies a constraint qualification which we need to derive an optimality condition. Thus it is very important to investigate an optimality condition for an efficient solution of a .