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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 65, 2016 - Issue 2
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Articles

Asymptotic optimality conditions for linear semi-infinite programming

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Pages 387-414 | Received 14 Oct 2014, Accepted 03 May 2015, Published online: 11 Jun 2015

References

  • López MA, Still G. Semi-infinite programming. Eur. J. Oper. Res. 2007;143:491–518.
  • Kortanek KO, Zhang Q. Perfect duality in semi-infinite and semi-definite programming. Math. Program. 2001;91:127–144.
  • Rubio JE. Optimal control problems with unbounded constraint sets. Optimization. 2000;48:191–210.
  • Slupphaug O, Imsland L, Foss A. Uncertainty modelling and robust output feedback control of nonlinear discrete systems: a mathematical programming approach. Int. J. Robust Nonlinear Control. 2000;10:1129–1152.
  • Liu Y, Ding MF. A ladder method for semi-infinite programming. J. Ind. Manag. Optim. 2014;10:397–412.
  • Puente R, Vera De Serio VN. Locally Farkas-Minkowski linear semi-infinite systems. TOP. 1999;7:103–121.
  • Goberna MA, López MA. Linear semi-infinite optimization. Chichester: Wiley; 1998.
  • Boţ RI, Wanka G. An alternative formulation for a new closed cone constraint qualification. Nonlinear Anal.: Theory Methods Appl. 2006;64:1367–1381.
  • Fajardo MD, López MA. Locally Farkas-Minkowski systems in convex semi-infinite programming. J. Optim. Theory Appl. 1999;103:313–335.
  • Li C, Zhao X, Hu Y. Quasi-Slater and Farkas-Minkowski qualifications for semi-infinite programming with applications. SIAM J. Optim. 2013;23:2208–2230.
  • Dinh N, Goberna MA, López MA, et al. New Farkas-type constraint qualifications in convex infinite programming. ESAIM Control Optim. Calc. Var. 2007;13:580–597.
  • Li C, Ng KF. On constraint qualification for an infinite system of convex inequalities in a Banach space. SIAM J. Optim. 2005;15:488–512.
  • Li C, Ng KF, Pong TK. Constraint qualifications for convex inequality systems with applications in constrained optimization. SIAM J. Optim. 2008;19:163–187.
  • Boţ RI, Csetnek ER, Wanka G. Sequential optimality conditions in convex programming via perturbation approach. J. Convex Anal. 2008;15:149–164.
  • Dinh N, Goberna MA, López MA, et al. Convex inequalities without constraint qualification nor closedness condition, and their applications in optimization. Set-valued Var. Anal. 2010;18:423–445.
  • Thibault L. Sequential convex subdifferential calculus and sequential Lagrange multipliers. SIAM J. Control Optim. 1997;35:1434–1444.
  • Goberna MA, López MA, Todorov MI. Extended active constraints in linear optimization with applications. SIAM J. Optim. 2003;14:806–619.
  • Martínez-Legaz JE, Todorov MI, Zetina C. γ-Active constraints in convex semi-infinite programming. Numer. Funct. Anal. Appl. 2014;35:1078–1094.
  • Liu Y. An exterior point method for linear programming based on inclusive normal cones. J. Ind. Manag. Optim. 2010;6:825–846.
  • Liu Y. Duality in linear programming: from trichotomy to quadrichotomy. J. Ind. Manag. Optim. 2011;7:1003–1011.

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