This article is cited in 8 scientific papers (total in 8 papers)
Optimality conditions and newton-type methods for mathematical programs with vanishing constraints
A. F. Izmailov, A. L. Pogosyan
Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
A new class of optimization problems is discussed in which some constraints must hold in certain regions of the corresponding space rather than everywhere. In particular, the optimal design of topologies for mechanical structures can be reduced to problems of this kind. Problems in this class are difficult to analyze and solve numerically because their constraints are usually irregular. Some known first- and second-order necessary conditions for local optimality are refined for problems with vanishing constraints, and special Newton-type methods are developed for solving such problems.
mathematical program with vanishing constraints, mathematical program with complementarity constraints, constraint qualification, optimality conditions, sequential quadratic programming, active-set method.
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Computational Mathematics and Mathematical Physics, 2009, 49:7, 1128–1140
A. F. Izmailov, A. L. Pogosyan, “Optimality conditions and newton-type methods for mathematical programs with vanishing constraints”, Zh. Vychisl. Mat. Mat. Fiz., 49:7 (2009), 1184–1196; Comput. Math. Math. Phys., 49:7 (2009), 1128–1140
Citation in format AMSBIB
\by A.~F.~Izmailov, A.~L.~Pogosyan
\paper Optimality conditions and newton-type methods for mathematical programs with vanishing constraints
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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A. F. Izmailov, A. L. Pogosyan, “A semismooth sequential quadratic programming method for lifted mathematical programs with vanishing constraints”, Comput. Math. Math. Phys., 51:6 (2011), 919–941
Izmailov A.F., Pogosyan A.L., “Active-set Newton methods for mathematical programs with vanishing constraints”, Comput. Optim. Appl., 53:2 (2012), 425–452
Dorsch D., Shikhman V., Stein O., “Mathematical programs with vanishing constraints: critical point theory”, J. Glob. Optim., 52:3 (2012), 591–605
Hoheisel T., Kanzow Ch., Schwartz A., “Mathematical programs with vanishing constraints: a new regularization approach with strong convergence properties”, Optimization, 61:6 (2012), 619–636
Achtziger W., Hoheisel T., Kanzow Ch., “A Smoothing-Regularization Approach to Mathematical Programs with Vanishing Constraints”, Comput. Optim. Appl., 55:3 (2013), 733–767
Hu Q., Chen Yu., Zhu Zh., Zhang B., “Notes on Convergence Properties For a Smoothing-Regularization Approach To Mathematical Programs With Vanishing Constraints”, Abstract Appl. Anal., 2014, 715015
Mishra S.K., Singh V., Laha V., “On duality for mathematical programs with vanishing constraints”, Ann. Oper. Res., 243:1-2 (2016), 249–272
Hu Q., Wang J., Chen Yu., Zhu Zh., “On an
l 1 exact penalty result for mathematical programs with vanishing constraints”, Optim. Lett., 11:3 (2017), 641–653
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