On the global convergence of interior-point nonlinear programming algorithms

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Caratheodory's lemma states that if we have a linear combination of vectors in R-n, we can rewrite this combination using a linearly independent subset. This lemma has been successfully applied in nonlinear optimization in many contexts. In this work we present a new version of this celebrated result, in which we obtained new bounds for the size of the coefficients in the linear combination and we provide examples where these bounds are useful. We show how these new bounds can be used to prove that the internal penalty method converges to KKT points, and we prove that the hypothesis to obtain this result cannot be weakened. The new bounds also provides us some new results of convergence for the quasi feasible interior point l(2)-penalty method of Chen and Goldfarb [7].292125138Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [05/02163-8

A Flexible Inexact-Restoration Method for Constrained Optimization

We introduce a new flexible inexact-restoration algorithm for constrained optimization problems. in inexact-restoration methods, each iteration has two phases. the first phase aims at improving feasibility and the second phase aims to minimize a suitable objective function. in the second phase, we also impose bounded deterioration of the feasibility, obtained in the first phase. Here, we combine the basic ideas of the Fischer-Friedlander approach for inexact-restoration with the use of approximations of the Lagrange multipliers. We present a new option to obtain a range of search directions in the optimization phase, and we employ the sharp Lagrangian as merit function. Furthermore, we introduce a flexible way to handle sufficient decrease requirements and an efficient way to deal with the penalty parameter. Global convergence of the new inexact-restoration method to KKT points is proved under weak constraint qualifications.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Universidade Federal de São Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP, BrazilUniv São Paulo, Inst Math & Stat, Dept Appl Math, São Paulo, SP, BrazilUniv Estadual Campinas, Inst Math Stat & Sci Comp, Dept Appl Math, Campinas, SP, BrazilUniversidade Federal de São Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP, BrazilCNPq: E-26/171.164/2003 - APQ1FAPESP: 2010/19720-5FAPESP: 2013/05475-7FAPESP: 201307375-0Web of Scienc

New sequential optimality conditions for mathematical programs with complementarity constraints and algorithmic consequences

In recent years, the theoretical convergence of iterative methods for solving nonlinearnconstrained optimization problems has been addressed using sequential optimality conditions, which are satisfied by minimizers independently of constraint qualifications (CQs). Even though there is a considerable literature devoted to sequential conditions for standard nonlinear optimization, the same is not true for mathematical programs with complementarity constraints (MPCCs). In this paper, we show that the established sequential optimality conditions are not suitable for the analysis of convergence of algorithms for MPCC. We then propose new sequential optimality conditions for usual stationarity concepts for MPCC, namely, weak, Clarke, and Mordukhovich stationarity. We call these conditions AW-, AC-, and AM-stationarity, respectively. The weakest MPCC-tailored CQs associated with them are also provided. We show that some of the existing methods for MPCC reach AC-stationary points, extending previous convergence results. In particular, the new results include the linear case, not previously covered.29432013230CNPQ - Conselho Nacional de Desenvolvimento Científico e TecnológicoFAPESP – Fundação de Amparo à Pesquisa Do Estado De São Paulo301888/2017-5; 306986/2016- 7; 302915/2016-82013/07375-0; 2013/05475-7; 2017/18308-

Einfluss einer nach Schadstoffimmission vermehrten Einstrahlung von UV-B-Licht auf den Ertrag von Kulturpflanzen (FKW 22). 1. Versuchsjahr

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