Strictly Increasing Positively Homogeneous Functions with Application to Exact Penalization

References

• Birkhoff , Q. 1967 . Lattice Theory, Vol. 25, , 3rd Edn. , AMS Colloqiuim Publications, AMS .
   Google Scholar
• Burke , J.V. 1991 . Calmness and exact penalization . SIAM J. Control and Optimization , 29 : 493 – 497 .
   Web of Science ®Google Scholar
• Burke , J.V. 1991 . An exact penalization viewpoint of constrained optimization . SIAM J. Control and Optimization , 29 : 968 – 988 .
   Web of Science ®Google Scholar
• Giannessi , F. and Mastroeni , M. 1999 . “ On the theory of vector optimization and variational inequalities. Image space analysis and separation ” . In Vector Variational Inequalities and Vector Equilibria. Mathematical Theories , Edited by: Giannessi , F. 153 – 215 . Dordrecht : Kluwer Academic Publisher .
   Google Scholar
• Goh , C.J. and Yang , X.Q. 2001 . A nonlinear Lagrangian theory for nonconvex optimization . J. Optimiz. Theory Appl. , 109 : 99 – 121 .
   Web of Science ®Google Scholar
• Huang , X.X. and Yang , X.Q. 2001 . Approximate optimal solutions and nonlinear Lagrangian functions . Journal of Global Optimization , 21 : 51 – 65 .
   Web of Science ®Google Scholar
• Li , D. 1995 . Zero duality gap for a class of nonconvex optimization problems . J. Optimization Theory and Appl. , 85 : 309 – 323 .
   Web of Science ®Google Scholar
• Kutateladze , A.M. and Rubinov , A.M. 1972 . Minkowski duality and its applications . Russian Math. Surveys , 27 : 137 – 191 .
   Google Scholar
• Luo , Z.Q. , Pang , J.S. and Ralph , D. 1996 . Mathematical Programs with Equilibrium Constraints , New York : Cambridge University Press .
   Google Scholar
• Makarov , V.L. , Levin , M.J. and Rubinov , A.M. 1995 . Mathematical Economic Theory: Pure and Mixed types of Economic Mechanisms , Amsterdam : North-Holland .
   Google Scholar
• Pallaschke , D. and Rolewicz , S. 1997 . Foundations of Mathematical Optimization , Dordrecht : Kluwer Academic Press .
   Google Scholar
• Rubinov , A.M. 2000 . Abstract Convexity and Global Optimization , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Rubinov , A.M. , Yang , X.Q. , Bagirov , A.M. and Gasimov , R. Lagrange-type Functions in Constrained Optimization (to appear)
   Google Scholar
• Rubinov , A.M. , Glover , B.M. and Yang , X.Q. 2000 . Decreasing functions with application to penaliza- tion . SIAM J. Optimization , 10 : 289 – 313 .
   Web of Science ®Google Scholar
• Rubinov , A.M. and Uderzo , A. 2001 . On global optimality conditions via separation functions . J. Optimization Theory and Appl. , 109 : 345 – 370 .
   Web of Science ®Google Scholar
• Rubinov , A.M. , Yang , X.Q. and Bagirov , A.M. 2002 . Nonlinear penalty functions with a small penalty parameter . Optimization Methods and Software , 17 : 931 – 964 .
   Web of Science ®Google Scholar
• Rubinov , A.M. , Huang , X.X. and Yang , X.Q. The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Function (to appear, Math, for Op. Res.).
   Google Scholar
• Singer , I. 1997 . Abstract Convex Analysis , New York : A Wiley-Interscience Publication .
   Google Scholar
• Wang , C.Y. , Yang , X. Q. and Yang , X.M. Nonlinear Lagrange Duality Theorems and Penalty Function ethods in Continuous Optimization (submitted paper)
   Google Scholar
• Yang , X.Q. and Huang , X.X. 2001 . A nonlinear Lagrangian approach to constrained optimization prob- ems . SIAM J. Optimization , 14 : 1119 – 1144 .
   Web of Science ®Google Scholar
• Yevtushenko , Yu. G. and Zhadan , V.G. 1990 . Exact auxiliary functions in optimization problems . S.S.R Comput. Maths. Math. Phys. , 30 : 31 – 42 .
   Web of Science ®Google Scholar