Metric Projection onto a Closed Set: Necessary and Sufficient Conditions for the Global Minimum

Published Online:https://doi.org/10.1287/moor.1050.0173

References

  • Beck A., Teboulle M. Global optimality conditions for quadratic optimization problems with binary constraints. SIAM J. Optim. (2000) 11:179–188CrossrefGoogle Scholar
  • Hiriart-Urruty J. B. Conditions for global optimality 2. J. Global Optim. (1998) 13:349–367CrossrefGoogle Scholar
  • Hiriart-Urruty J. B. Global optimality conditions in maximizing a convex quadratic function under convex quadratic constraints. J. Global Optim. (2001) 21:445–455CrossrefGoogle Scholar
  • Luc D. T.Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems (1989) Vol. 319(Springer-Verlag, Berlin, Germany) Google Scholar
  • Martinez-Legaz J.-E., Rubinov A. M., Singer I. Downward sets and their separation and approximation properties. J. Global Optim. (2002) 23:111–137CrossrefGoogle Scholar
  • Mohebi H., Rubinov A. M. Best approximation by downward sets with applications. Anal. Theory Appl. (2005) . ForthcomingGoogle Scholar
  • Pan X.-C., Zheng Q. Global optimum shape design. Comput. Math. Appl. (1999) 37:151–162CrossrefGoogle Scholar
  • Pinar M. C. Sufficient global optimality conditions for bivalent quadratic optimization. J. Optim. Theory Appl. (2004) 122:443–440CrossrefGoogle Scholar
  • Rubinov A. M. Sublinear operators and their applications. Uspehi Mat. Nauk (Russian Math. Surveys) (1977) 32:113–174Google Scholar
  • Rubinov A. M.Abstract Convexity and Global Optimization (2000) (Kluwer Academic Publishers, Dordrecht, The Netherlands) CrossrefGoogle Scholar
  • Rubinov A. M., Singer I. Topical and sub-topical functions, downward sets and abstract convexity. Optimization (2001) 50:307–351CrossrefGoogle Scholar
  • Singer I.Abstract Convex Analysis (1987) (Wiley-Interscience, New York) Google Scholar
  • Strekolovsky A. S. Global optimality conditions for nonconvex optimization. J. Global Optim. (1998) 12:415–434CrossrefGoogle Scholar
  • Strekolovsky A. S.Elements of Nonconvex Optimization (2003) (Nauka, Novosibirsk, Russia) . (In Russian.)Google Scholar
  • Tsevendorj I. Piecewice-convex maximization problems: Global optimality conditions. J. Global Optim. (2001) 21:1–14CrossrefGoogle Scholar
  • Vulikh B. Z.Introduction to the Theory of Partially Ordered Vector Spaces (1967) (Wolters-Noordhoff, Groningen, The Netherlands) Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.