Newton-type methods for mathematical programs with vanishing constraintsтезисы доклада

Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.

Работа с тезисами доклада

[1] Izmailov A. F., Pogosyan A. L. Newton-type methods for mathematical programs with vanishing constraints // Proceedings of the Eighth World Congress on Structural and Multidisciplinary Optimization (WCSMO-8). — International Society for Structural and Multidisciplinary Optimization Lisbon, 2009. — P. 79. We consider a class of optimization problems with vanishing constraints, which is a relatively new problem setting, very appropriate for modelling some optimal topology design problems of mechanical structures. The specificity of this setting is that it contains constraints that are being imposed (switched on) at some points of the feasible region, while being disregarded (switched off) at other points. This is a convenient framework for modelling the structures where some restrictions apply only to those "parts" of the potential structure where the material is present, and do not apply otherwise. The fact that some constraints "vanish" from the problem at certain points, gave rise to the name of mathematical programs with vanishing constraints (MPVC). Problems of this class are difficult from both analytical and numerical points of view, because such problems are usually degenerate at a solution. They are somewhat related to but structurally different from the well-studied class of mathematical programs with complementarity constraints. In this work, we derive first- and second-order necessary optimality conditions for MPVC under the assumptions weaker than those previously used in the literature this context. Furthermore, we suggest and analyze two classes of special Newton-type methods for MPVC, possessing local superlinear convergence under natural assumptions: the so-called piecewise SQP method, and the active-set method, the latter being more appropriate for potential globalization of its convergence.

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