Optimality Conditions and Characterizations of the Solution Sets in Generalized Convex Problems and Variational Inequalities (original) (raw)

Access this article

Log in via an institution

Subscribe and save

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

1. Mangasarian, O.L.: A simple characterization of solution sets of convex programs. Oper. Res. Lett. 7, 21–26 (1988)
   Article MathSciNet MATH Google Scholar
2. Burke, J.V., Ferris, M.C.: Characterization of the solution sets of convex programs. Oper. Res. Lett. 10, 57–60 (1991)
   Article MathSciNet MATH Google Scholar
3. Jeyakumar, V.: Infinite dimensional convex programming with applications to constrained approximation. J. Optim. Theory Appl. 75, 469–586 (1992)
   Article MathSciNet Google Scholar
4. Jeyakumar, V., Yang, X.Q.: Convex composite multiobjective nonsmooth programming. Math. Program. 59, 325–343 (1993)
   Article MathSciNet MATH Google Scholar
5. Jeyakumar, V., Yang, X.Q.: On characterizing the solution sets of pseudolinear programs. J. Optim. Theory Appl. 87, 747–755 (1995)
   Article MathSciNet MATH Google Scholar
6. Lalitha, C.S., Mehta, M.: Characterization of the solution sets of pseudolinear programs and pseudoaffine variational inequality problems. J. Nonlinear Convex Anal. 8, 87–98 (2007)
   MathSciNet MATH Google Scholar
7. Smietanski, M.: A note on characterization of solution sets to pseudolinear programming problems. Appl. Anal. (2011). doi:10.1080/00038811.2011.584184
   Google Scholar
8. Ivanov, V.I.: Characterizations of the solution sets of generalized convex minimization problems. Serdica Math. J. 29, 1–10 (2003)
   MathSciNet MATH Google Scholar
9. Wu, Z.: The convexity of the solution set of a pseudoconvex inequality. Nonlinear Anal. 69, 1666–1674 (2008)
   Article MathSciNet MATH Google Scholar
10. Bianchi, M., Schaible, S.: An extension of pseudolinear functions and variational inequality problems. J. Optim. Theory Appl. 104, 59–71 (2000)
    Article MathSciNet MATH Google Scholar
11. Ivanov, V.I.: Optimization and variational inequalities with pseudoconvex functions. J. Optim. Theory Appl. 146, 602–616 (2010)
    Article MathSciNet MATH Google Scholar
12. Wu, Z.L., Wu, S.Y.: Characterizations of the solution sets of convex programs and variational inequality problems. J. Optim. Theory Appl. 130, 339–358 (2006)
    Article MathSciNet MATH Google Scholar
13. Jeyakumar, V., Lee, G.M., Dinh, N.: Lagrange multiplier conditions characterizing the optimal solution set of cone-constrained convex programs. J. Optim. Theory Appl. 123, 83–103 (2004)
    Article MathSciNet MATH Google Scholar
14. Penot, J.-P.: Characterization of solution sets of quasiconvex programs. J. Optim. Theory Appl. 117, 627–636 (2003)
    Article MathSciNet MATH Google Scholar
15. Dinh, N., Jeyakumar, V., Lee, G.M.: Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems. Optimization 55, 241–250 (2006)
    Article MathSciNet MATH Google Scholar
16. Lalitha, C.S., Mehta, M.: Characterizations of solution sets of mathematical programs in terms of Lagrange multipliers. Optimization 58, 995–1007 (2009)
    Article MathSciNet MATH Google Scholar
17. Mangasarian, O.L.: Nonlinear Programming. Classics in Applied Mathematics, vol. 10. SIAM, Philadelphia (1994)
    Book MATH Google Scholar
18. Gordan, P.: Über die Auflösungen linearer Gleichungen mit reelen coefficienten. Math. Ann. 6, 23–28 (1873)
    Article MathSciNet MATH Google Scholar
19. Giorgi, G., Guerraggio, A., Thierfelder, J.: Mathematics of Optimization. Elsevier, Amsterdam (2004)
    MATH Google Scholar
20. Bazaraa, M.S., Shetty, C.M.: Nonlinear Programming—Theory and Algorithms. Wiley, New York (1979)
    MATH Google Scholar
21. Ginchev, I., Ivanov, V.I.: Higher-order pseudoconvex functions. In: Konnov, I.V., Luc, D.T., Rubinov, A.M. (eds.) Proc. 8th Int. Symp. on Generalized Convexity/Monotonicity. Lecture Notes in Econom. and Math. Systems, vol. 583, pp. 247–264. Springer, Berlin (2007)
    Google Scholar
22. Ginchev, I., Ivanov, V.I.: Second-order optimality conditions for problems with C1 data. J. Math. Anal. Appl. 340, 646–657 (2008)
    Article MathSciNet MATH Google Scholar
23. Karamardian, S.: Complementarity problems over cones with monotone and pseudomonotone maps. J. Optim. Theory Appl. 18, 445–454 (1976)
    Article MathSciNet MATH Google Scholar
24. Harker, P.T., Pang, J.S.: Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Program. 48, 161–220 (1990)
    Article MathSciNet MATH Google Scholar
25. Marcotte, P., Zhu, D.: Weak sharp solutions of variational inequalities. SIAM J. Optim. 9, 179–189 (1998)
    Article MathSciNet Google Scholar
26. Crouzeix, J.-P., Marcotte, P., Zhu, D.: Conditions ensuring the applicability of cutting plane methods for solving variational inequalities. Math. Program., Ser. A 88, 521–539 (2000)
    Article MathSciNet MATH Google Scholar

Download references