Solution of a truss topology bilevel programming problem by means of an inexact restoration method

We formulate a truss topology optimization problem as a bilevel programming problem and solve it by means of a line search type inexact restoration algorithm. We discuss details of the implementation and show results of numerical experiments.We formulate a truss topology optimization problem as a bilevel programming problem and solve it by means of a line search type inexact restoration algorithm. We discuss details of the implementation and show results of numerical experiments.301109125CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPERJ - FUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIROFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOE-26/171.164/2003-APQ106/53768-

Economic inexact restoration for derivative-free expensive function minimization and applications

The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact Restoration framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low- and high-precision evaluations. In the present research, it is recognized that many problems with expensive objective functions are nonsmooth and, sometimes, even discontinuous. Having this in mind, the Inexact Restoration approach is extended to the nonsmooth or discontinuous case. Although optimization phases that rely on smoothness cannot be used in this case, basic convergence and complexity results are recovered. A derivative-free optimization phase is defined and the subproblems that arise at this phase are solved using a regularization approach that take advantage of different notions of stationarity. The new methodology is applied to the problem of reproducing a controlled experiment that mimics the failure of a dam

Assessing the reliability of general-purpose Inexact Restoration methods

Inexact Restoration methods have been proved to be effective to solve constrained optimization problems in which some structure of the feasible set induces a natural way of recovering feasibility from arbitrary infeasible points. Sometimes natural ways of dealing with minimization over tangent approximations of the feasible set are also employed. A recent paper Banihashemi and Kaya (2013)] suggests that the Inexact Restoration approach can be competitive with well-established nonlinear programming solvers when applied to certain control problems without any problem-oriented procedure for restoring feasibility. This result motivated us to revisit the idea of designing general-purpose Inexact Restoration methods, especially for large-scale problems. In this paper we introduce affordable algorithms of Inexact Restoration type for solving arbitrary nonlinear programming problems and we perform the first experiments that aim to assess their reliability. Initially, we define a purely local Inexact Restoration algorithm with quadratic convergence. Then, we modify the local algorithm in order to increase the chances of success of both the restoration and the optimization phase. This hybrid algorithm is intermediate between the local algorithm and a globally convergent one for which, under suitable assumptions, convergence to KKT points can be proved28

Two new weak constraint qualifications and applications

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.Facultad de Ciencias ExactasDepartamento de Matemátic

Inexact restoration method for derivative-free optimization with smooth constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the inexact restoration framework, by means of which each iteration is divided in two phases. In the first phase one considers only the constraints, in order to improve feasibility. In the second phase one minimizes a suitable objective function subject to a linear approximation of the constraints. The second phase must be solved using derivative-free methods. An algorithm introduced recently by Kolda, Lewis, and Torczon for linearly constrained derivative-free optimization is employed for this purpose. Under usual assumptions, convergence to stationary points is proved. A computer implementation is described and numerical experiments are presented.A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the inexact restoration framework, by means of23211891213CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPERJ - FUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIROFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [E-26/171.164/2003-APQ1]FAPESP [FAPESP 2011-51305-0]FAPESP [03/09169-6, 06/53768-0, 07/06663-0, 08/00468-4]E-26/171.164/2003–APQ12011-51305-0; 03/09169-6; 06/53768-0; 07/06663-0; 08/00468-4sem informaçãoWe are indebted to associate editor Prof. Margaret Wright and two anonymous referees for many useful comments and remarks that led to significant improvement of this pape

A new line search inexact restoration approach for nonlinear programming

Nonlinear programming, Inexact restoration, Line search, Penalty function, Complementarity constraints,