Continuity of parametric mixed-integer quadratic programs and its application to stability analysis of two-stage quadratic stochastic programs with mixed-integer recourse

References

• Markowitz H. Portfolio selection. J. Finance. 1952;7:77–91.
   Web of Science ®Google Scholar
• Nocedal J, Wright SJ. Numerical optimization. Berlin: Springer; 1999.
   Google Scholar
• Xu CX, Chen ZP, Li NC. Modern optimization methods. Beijing: Science Press; 2002 [Chinese].
   Google Scholar
• Yuan Y. Computational methods for nonlinear optimization. Beijing: Science Press; 2008 [Chinese].
   Google Scholar
• Bank B, Guddat J, Klatte D, Kummer B, Tammer K. Non-linear parametric optimization. Berlin: Akademie Verlag; 1982.
   Google Scholar
• Berkelaar AB, Jansen B, Roos K, Terlaky T. Sensitivity analysis in (degenerate) quadratic programming. Research Report, Rotterdam: Erasmus University; 1996.
   Google Scholar
• Best MJ, Chakravarti N. Stability of linearly constrained convex quadratic programs. J. Optim. Theory Appl. 1990;64:43–53.
   Web of Science ®Google Scholar
• Best MJ, Ding B. On the continuity of the minimum in parametric quadratic programs. J. Optim. Theory Appl. 1995;86:245–250.
   Web of Science ®Google Scholar
• Eaves BC. On quadratic programming. Manage. Sci. 1971;17:698–711.
   Google Scholar
• Hadigheh AG, Romanko O, Terlaky T. Sensitivity analysis in convex quadratic optimization: simultaneous perturbation of the objective and right-hand-side vectors. Research Report No. 2003/6, Hamilton: McMaster University; 2003.
   Google Scholar
• Lee GM, Tam NN, Yen ND. On the optimal value function of a linearly perturbed quadratic program. J. Glob. Optim. 2005;32:119–134.
   Web of Science ®Google Scholar
• Lee GM, Tam NN, Yen ND. Continuity of the solution map in quadratic programs under linear perturbations. J. Optim. Theory Appl. 2006;129:415–423.
   Web of Science ®Google Scholar
• Phu HX, Yen ND. On the stability of solutions to quadratic programming problems. Math. Program. 2001;89:358–394.
   Web of Science ®Google Scholar
• Tam NN. Continuity of the optimal value function in indefinite quadratic programming. J. Glob. Optim. 2002;23:43–61.
   Web of Science ®Google Scholar
• Tam NN, Yen ND. Continuity properties of the Karush-Kuhn-Tucker point set in quadratic programming problems. Math. Program. 1999;85:193–206.
   Web of Science ®Google Scholar
• Daniel JW. Stability of the solution of definite quadratic programs. Math. Program. 1973;5:41–53.
   Google Scholar
• Klatte D. On the Lipschitz behavior of optimal solutions in parametric problems of quadratic optimization and linear complementarity. Optimization. 1985;16:819–831.
   Google Scholar
• Bank B, Hansel R. Stability of mixed-integer quadratic programming problems. Math. Program. 1984;21:1–17.
   Web of Science ®Google Scholar
• Chen Z, Han Y. Quantitative stability of mixed-integer two-stage quadratic stochastic programs. Math. Methods Oper. Res. 2012;75:149–163.
   Web of Science ®Google Scholar
• Römisch W, Schultz R. Distribution sensitivity in stochastic programming. Math. Program. 1991;50:197–226.
   Web of Science ®Google Scholar
• Chen Z, Xu Z. Continuity and stability of two-stage quadratic stochastic programs with mixed-integer recourse. Numer. Func. Anal. Opt. 2009;30:462–477.
   Web of Science ®Google Scholar
• Schultz R. Rates of convergence in stochastic programs with complete integer recourse. SIAM J. Optim. 1996;6:1138–1152.
   Web of Science ®Google Scholar
• Rachev ST, Römisch W. Quantitative stability in stochastic programming: The methods of probability metrics. Math. Oper. Res. 2002;27:792–818.
   Web of Science ®Google Scholar
• Römisch W. Stability of stochastic programming. In Rusczyński A, Shapiro A,editors. Stochastic programming. Handbooks in OR & MS. vol. 10. North-Holland, Amsterdam: Elsevier; 2003.
   Google Scholar
• Schultz R. On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Math. Program. 1995;70:73–89.
   Web of Science ®Google Scholar
• Qi L, Womersley RS. An SQP algorithm for extended linear-quadratic problems in stochastic programming. Ann. Oper. Res. 1995;56:251–285.
   Web of Science ®Google Scholar
• Mangasarian OL, Shiau TH. Lipschitz continuity of solutions of linear inequalities, programs, and complementary problems. SIAM J. Control Optim. 1987;25:583–595.
   Web of Science ®Google Scholar
• Granot F, Skorin-Kapov J. Some proximity and sensitivity in quadratic integer programming. Math. Program. 1990;47:259–268.
   Web of Science ®Google Scholar
• Cottle FW, Pang J-S, Stone RE. The linear complementarity problem. Boston (MA): Academic Press; 1992.
   Google Scholar
• Klatte D, Thiere G. Error bounds for solutions of linear equations and inequalities. ZOR-Math. Method Oper. Res. 1995;41:191–214.
   Google Scholar
• Rockafeller RT, Wets RJ-B. Variational analysis. Berlin: Springer; 1998.
   Google Scholar