Journal ArticleDOI
On the computer implementation of feasible direction interior point algorithms for nonlinear optimization
J. Herskovits,G. Santos +1 more
TLDR
The paper discusses the computer implementation of a class of interior point algorithms for the minimization of nonlinear functions with equality and inequality constraints and the algorithms employed for the constrained line search and also with the quasi-Newton matrix updating.Abstract:
The paper discusses the computer implementation of a class of interior point algorithms for the minimization of nonlinear functions with equality and inequality constraints. These algorithms consist of fixed point iterations to solve KKT firstorder optimality conditions. At each iteration a descent direction is defined by solving a linear system. Then, the linear system is perturbed in such a way as to deflect the descent direction and obtain a feasible descent direction. A line search is finally performed to obtain a new interior point with a lower objective. Newton, quasi-Newton, or first-order versions of the algorithm can be obtained. This paper is mainly concerned with the solution of the internal linear systems, the algorithms that are employed for the constrained line search and also with the quasi-Newton matrix updating. Some numerical results obtained with a quasi Newton algorithm are also presented. A set of test problems were solved very efficiently with the same values of the internal parameters.read more
Citations
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A two-stage feasible direction algorithm for non linearly constrained optimization
TL;DR: Although the present version of the algorithm does not include any second-order information, like quasi-Newton methods, these numerical results exhibit a behavior comparable to that of the best methods known at present for nonlinear programming.
Journal ArticleDOI
Model-reduction techniques for reliability-based design problems of complex structural systems
TL;DR: A model reduction technique combined with an appropriate optimization scheme is proposed to carry out the design process efficiently in a reduced space of generalized coordinates for reliability-based design problems of a class of linear and nonlinear finite element models under stochastic excitation.
Journal ArticleDOI
Shape structural optimization with an interior point nonlinear programming algorithm
TL;DR: The aim of this paper is to study the implementation of an efficient and reliable technique for shape optimization of solids, based on general nonlinear programming algorithms, and to conclude that the present approach is simple to formulate and to code.
Journal ArticleDOI
Reliability-based design optimization of structural systems under stochastic excitation: An overview
TL;DR: In this article , the authors present a brief survey on some of the latest developments in the area of reliability-based design optimization of structural systems under stochastic excitation, which can be grouped into three main categories, namely, sequential optimization approaches, search based techniques, and schemes based on augmented reliability spaces.
Journal ArticleDOI
Reliability-Based Design Optimization of Uncertain Stochastic Systems: Gradient-Based Scheme
TL;DR: In this article, a nonlinear interior point algorithm and a line search strategy are used for reliability-based optimization of uncertain structural systems under stochastic excitation, and the results show that only a small number of reliability estimates have to be performed during the entire design process.
References
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