Geodesic
A semismooth sequential quadratic programming method for lifted mathematical programs with vanishing constraints
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 983-1006

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Mathematical programs with vanishing constraints are a difficult class of optimization problems with important applications to optimal topology design problems of mechanical structures. Recently, they have attracted increasingly more attention of experts. The basic difficulty in the analysis and numerical solution of such problems is that their constraints are usually nonregular at the solution. In this paper, a new approach to the numerical solution of these problems is proposed. It is based on their reduction to the socalled lifted mathematical programs with conventional equality and inequality constraints. Special versions of the sequential quadratic programming method are proposed for solving lifted problems. Preliminary numerical results indicate the competitiveness of this approach. 
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     author = {A. F. Izmailov and A. L. Pogosyan},
     title = {A~semismooth sequential quadratic programming method for lifted mathematical programs with vanishing constraints},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {983--1006},
     publisher = {mathdoc},
     volume = {51},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a2/}
}
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A. F. Izmailov; A. L. Pogosyan. A semismooth sequential quadratic programming method for lifted mathematical programs with vanishing constraints. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 983-1006. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a2/