Место издания:International Society for Structural and Multidisciplinary Optimization Lisbon
Первая страница:79
Аннотация: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.