Journal ArticleDOI
Rate of Convergence of a Class of Methods of Feasible Directions
Olivier Pironneau,Elijah Polak +1 more
TLDR
In this article, the authors studied the convergence rate of four methods of feasible directions of the Zoutendijk procedures 1 and 2 and two modifications of these procedures due to the authors.Abstract:
This paper deals with the rate of convergence of four methods of feasible directions the Zoutendijk procedures 1 and 2 and two modifications of these procedures due to the authors. It is shown that of these methods, the two due to the authors converge linearly under convexity assumptions, that the Zoutendijk procedure 2 converges sublinearly under these assumptions, and that the Zoutendijk procedure 1 converges linearly provided the solution of the problem is a vertex of the constraint set.read more
Citations
More filters
Journal ArticleDOI
On optimum design in fluid mechanics
TL;DR: In this article, the change in energy dissipation due to a small hump on a body in a uniform steady flow is calculated, and the result is used in conjunction with the variational methods of optimal control to obtain the optimality conditions for four minimum-drag problems of fluid mechanics.
Journal ArticleDOI
A survey of optimization techniques for integrated-circuit design
TL;DR: This work surveys contemporary optimization techniques and relates these to optimization problems which arise in the design of integrated circuits, and focuses on those multiobjective constrained optimization techniques which are appropriate to this environment.
Journal ArticleDOI
An Algorithm for Constrained Optimization with Semismooth Functions
TL;DR: The method is based on combining, modifying and extending the nonsmooth optimization work of Wolfe, Leraarechal, Feuer, Poljak and Merrill and can be thought of as a generalized reset conjugate gradient algorithm.
Journal ArticleDOI
An improved algorithm for optimization problems with functional inequality constraints
TL;DR: The algorithm presented was developed as an improved version of the Polak-Mayne algorithm; by performing certain approximations in a different way it was possible to eliminate an expensive test required by Polak and Mayne.
Journal ArticleDOI
An Infeasible Bundle Method for Nonsmooth Convex Constrained Optimization without a Penalty Function or a Filter
TL;DR: This paper demonstrates that the use of a parametrized penalty function in nonsmooth convex optimization can be avoided without using the relatively complex filter methods and proposes an approach which appears to be more direct and easier to implement, in the sense that it is closer in spirit and structure to the well-developed unconstrained bundle methods.
References
More filters
Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
Journal ArticleDOI
Bimatrix Equilibrium Points and Mathematical Programming
TL;DR: In this paper, simple constructive proofs are given of solutions to the matric matric system Mz − ω = q; z ≧ 0; ω ≧ 1; zT = 0, for various kinds of data M, q, which embrace quadratic programming and the problem of finding equilibrium points of bimatrix games.
Journal ArticleDOI
A Duality Theorem for Nonlinear Programming
TL;DR: In this paper, the authors established a dual to the nonlinear programming problem of which a solution may be easily obtained, which then helps to obtain a solution of the original problem.
Journal ArticleDOI
On the Convergence of Some Feasible Direction Algorithms for Nonlinear Programming
TL;DR: In this paper, the authors consider the problem of determining conditions on the selection of directions in feasible direction algorithms for unconstrained maximization problems which assure the gradient vanishes in the limit.