A parametric characterization of local optimality

被引：10
作者：
Mirjam Dür
机构：
[1] Department of Statistics, Vienna University of Economics, A-1090 Vienna
来源：
Mathematical Methods of Operations Research | 2003年 / 57卷 / 1期
关键词：
ε-subdifferentials; Convex analysis; Global optimality conditions; Local optimality conditions;
D O I：
10.1007/s001860200232
中图分类号：
学科分类号：
摘要：
In a series of papers, Hiriart-Urruty proposed necessary and sufficient global optimality conditions for the so-called d.c. problem and the convex maximization problem. In this paper, we investigate the underlying local optimality conditions, which, in general, are necessary, but not sufficient conditions. We establish sufficient local optimality conditions related to Hiriart-Urruty's conditions and discuss the meaning of a certain critical parameter value appearing in this condition. © Springer-Veriag 2003.
引用
收藏
页码：101 / 109
页数：8
相关论文
共 15 条
[1]  
Bomze I.M., Branch-and-bound approaches to standard quadratic optimization problems, Journal of Global Optimization, 22, pp. 17-37, (2002)
[2]  
Bomze I.M., Locatelli M., A characterization of undominated D.C. decompositions of quadratic functions, Technical Report No. 2001-12, 2001, 12
[3]  
Dur M., Conditions characterizing minima of the difference of convex functions, Monatshefte für Mathematik, 134, pp. 295-303, (2002)
[4]  
Dur M., Horst R., Locatelli M., Necessary and sufficient global optimality conditions for convex maximization revisited, Journal of Mathematical Analysis and Applications, 217, pp. 637-649, (1998)
[5]  
Flores-Bazan F., On minima of the difference of functions, Journal of Optimization Theory and Applications, 93, pp. 525-531, (1997)
[6]  
Hiriart-Urruty J.-B., From convex optimization to nonconvex optimization, Necessary and Sufficient Conditions for Global Optimality, pp. 219-239, (1989)
[7]  
Hiriart-Urruty J.-B., Conditions for global optimality, Handbook of Global Optimization, pp. 1-26, (1995)
[8]  
Hiriart-Urruty J.-B., Lemarechal C., Convex analysis and minimization algorithms I and II, Grundlehren der Mathematischen Wissenschaften, 305-306, (1996)
[9]  
Horst R., Pardalos P.M., Thoai N.V., Introduction to Global Optimization, (2000)
[10]  
Singer I., A fenchel-rockafellar type duality theorem for maximization, Bulletin of the Australian Mathematical Society, 20, pp. 193-198, (1979)
12