Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 71, 2022 - Issue 7
113
Views
0
CrossRef citations to date
0
Altmetric
Articles

Existence and sensitivity analysis for nonconvex cubic optimization problems

&
Pages 1883-1906 | Received 01 Nov 2019, Accepted 28 Sep 2020, Published online: 23 Nov 2020

References

  • Lee GM, Tam NN, Yen ND. Quadratic programming and affine variational inequalities: a qualitative study. New York (NY): Springer-Verlag; 2005. (Nonconvex Optimization and Its Application; 78).
  • Henin C, Doutriaux J. A specialization of the convex simplex method to cubic programming. Decis Econ Finance. 1980;3(2):61–72.
  • Schaible S. Quasi concavity and pseudo concavity of cubic functions. Math Program. 1973;5:243–247.
  • Andronov VG. On solvability of the problem of polynomial programming (in Russian). Izvestija Akadem Nauk SSSR, Tekhnicheskaja Kibernetika. 1982;4:194–197. Translation appeared in News of the Academy of Science of USSR, Department of Technical Sciences, Technical Cybernetics.
  • Klatte D. On a Frank–Wolfe type theorem in cubic optimization. Optimization. 2019;68:539–547.
  • Wang Y, Liang Z. Global optimality conditions for cubic minimization problem with box or binary constraints. J Glob Optim. 2010;47(4):583–595.
  • Wu ZY, Quan J, Li GQ, et al. Necessary optimality conditions and new optimization methods for cubic polynomial optimization problems with mixed variables. J Optim Theory Appl. 2012;153(2):408–435.
  • Zhang X, Wang Y, Ma W. Global sufficient optimality conditions for a special cubic minimization problem. Math Problems Eng. 2012;2012. Article ID 871741.
  • Auslender A, Cominetti R. First and second order sensitivity analysis of nonlinear programs under directional constraint qualification conditions. Optimization. 1990;21:351–363.
  • Minchenko LI, Tarakanov A. On second-order directional derivatives of value functions. Optimization. 2015;64:389–407.
  • Bondarevsky V, Leschov A, Minchenko L. Value functions and their directional derivatives in parametric nonlinear programming. J Optim Theory Appl. 2016;171(2):440–464.
  • Bonnans JF, Shapiro A. Perturbation analysis of optimization problems. New York (NY): Springer-Verlag; 2000.
  • Bank B, Guddat J, Klatte D, et al. Nonlinear parametric optimization. Berlin: Akademie-Verlag; 1982.
  • Dempe S. Foundations of bilevel programming. Springer Science and Business Media; 2002.
  • Minchenko LI, Sakochik PP. Holder behavior of optimal solutions and directional differentiability of marginal functions in nonlinear programming. J Optim Theory Appl. 1996;90:555–580.
  • Nghi TV, Tam NN. Continuity and directional differentiability of the value function in parametric quadratically constrained nonconvex quadratic programs. Acta Math Vietnam. 2017;42:311–336.
  • Nghi TV. Coderivatives related to parametric extended trust region subproblem and their applications. Taiwanese J Math. 2018;22(2):485–511.
  • Nghi TV. On stability of solutions to parametric generalized affine variational inequalities. Optimization. 2018;67(2):269–285.
  • Tam NN, Nghi TV. On the solution existence and stability of quadratically constrained nonconvex quadratic programs. Optim Lett. 2018;12:1045–1063.
  • Nghi TV, Tam NN. Stability for parametric extended trust region subproblems. Pac J Optim. 2019;15(1):111–129.
  • Tam NN. Continuity of the optimal value function in indefinite quadratic programming. J Glob Optim. 2002;23:43–61.
  • Tam NN. Directional differentiability of the optimal value function in indefinite quadratic programming. Acta Math Vietnam. 2001;26:377–394.
  • Xu Y, Gu W, Huang H. Solvability of two classes of tensor complementarity problems. Math Problems Eng. 2019;2019:Article ID 6107517.
  • Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
  • Luo ZQ, Pang JS, Ralph D. Mathematical programs with equilibrium constraints. Cambridge: Cambridge University Press; 1996.
  • Gollan B. On the marginal function in nonlinear programming. Math Oper Res. 1984;9:208–221.
  • Gauvin J. A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming. Math Program. 1977;12:136–138.
  • Eaves BC. On quadratic programming. Manag Sci. 1971;17:698–711.
  • Baccari A. On the classical necessary second-order optimality conditions. J Optim Theory Appl. 2004;123:213–221.
  • Gauvin J, Dubeau F. Differential properties of the marginal function in mathematical programming. Math Program Study. 1982;19:101–119.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.