2,068 research outputs found
Linear complementarity problems on extended second order cones
In this paper, we study the linear complementarity problems on extended
second order cones. We convert a linear complementarity problem on an extended
second order cone into a mixed complementarity problem on the non-negative
orthant. We state necessary and sufficient conditions for a point to be a
solution of the converted problem. We also present solution strategies for this
problem, such as the Newton method and Levenberg-Marquardt algorithm. Finally,
we present some numerical examples
A sequential semidefinite programming method and an application in passive reduced-order modeling
We consider the solution of nonlinear programs with nonlinear
semidefiniteness constraints. The need for an efficient exploitation of the
cone of positive semidefinite matrices makes the solution of such nonlinear
semidefinite programs more complicated than the solution of standard nonlinear
programs. In particular, a suitable symmetrization procedure needs to be chosen
for the linearization of the complementarity condition. The choice of the
symmetrization procedure can be shifted in a very natural way to certain linear
semidefinite subproblems, and can thus be reduced to a well-studied problem.
The resulting sequential semidefinite programming (SSP) method is a
generalization of the well-known SQP method for standard nonlinear programs. We
present a sensitivity result for nonlinear semidefinite programs, and then
based on this result, we give a self-contained proof of local quadratic
convergence of the SSP method. We also describe a class of nonlinear
semidefinite programs that arise in passive reduced-order modeling, and we
report results of some numerical experiments with the SSP method applied to
problems in that class
On the resolution of the generalized nonlinear complementarity problem
Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem ( GNCP) defined on a polyhedral cone. It is not necessary to calculate projections that complicate and sometimes even disable the implementation of algorithms for solving these kinds of problems. Theoretical results that relate stationary points of the function that is minimized to the solutions of the GNCP are presented. Perturbations of the GNCP are also considered, and results are obtained related to the resolution of GNCPs with very general assumptions on the data. These theoretical results show that local methods for box-constrained optimization applied to the associated problem are efficient tools for solving the GNCP. Numerical experiments are presented that encourage the use of this approach.Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem ( GNCP) defined on a polyhedral cone. It is not necessary to calculate projections that complicate an122303321CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOsem informaçãosem informaçã
Generic identifiability and second-order sufficiency in tame convex optimization
We consider linear optimization over a fixed compact convex feasible region
that is semi-algebraic (or, more generally, "tame"). Generically, we prove that
the optimal solution is unique and lies on a unique manifold, around which the
feasible region is "partly smooth", ensuring finite identification of the
manifold by many optimization algorithms. Furthermore, second-order optimality
conditions hold, guaranteeing smooth behavior of the optimal solution under
small perturbations to the objective
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