Journal ArticleDOI
An exact penalty function method with global convergence properties for nonlinear programming problems
TLDR
A new continuously differentiable exact penalty function is introduced for the solution of nonlinear programming problems with compact feasible set that is defined on a suitable bounded open set containing the feasible region and that it goes to infinity on the boundary of this set.Abstract:
In this paper a new continuously differentiable exact penalty function is introduced for the solution of nonlinear programming problems with compact feasible set A distinguishing feature of the penalty function is that it is defined on a suitable bounded open set containing the feasible region and that it goes to infinity on the boundary of this set This allows the construction of an implementable unconstrained minimization algorithm, whose global convergence towards Kuhn-Tucker points of the constrained problem can be establishedread more
Citations
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Journal ArticleDOI
Nonlinear complementarity as unconstrained and constrained minimization
TL;DR: Preliminary numerical tests on two small nonmonotone problems from the published literature converged to degenerate or nondegenerate solutions from all attempted starting points in 7 to 28 steps of a BFGS quasi-Newton method for unconstrained optimization.
Journal ArticleDOI
Global optimization methods for engineering applications: A review
TL;DR: A review of the methods for global optimization reveals that most methods have been developed for unconstrained problems and need to be extended to general constrained problems because most of the engineering applications have constraints.
Journal ArticleDOI
Multiplier methods for engineering optimization
TL;DR: The theory and computational procedures of the multiplier methods used to solve the constrained engineering optimization problem are reviewed so that more efficient and effective ones can be developed for engineering applications.
Book ChapterDOI
Exact Penalty Methods
TL;DR: It is shown that, by making use of continuously differentiable functions that possess exactness properties, it is possible to define implementable algorithms that are globally convergent with superlinear convergence rate towards KKT points of the constrained problem.
Journal ArticleDOI
A smooth method for the finite minimax problem
TL;DR: It is proved that, under usual assumptions, it is possible to construct a continuously differentiable function, whose minimizers yield the minimizers of the max function and the corresponding minimum values.
References
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Book
Nonlinear Programming: Sequential Unconstrained Minimization Techniques
TL;DR: This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere.
Book
Nonlinear Programming
TL;DR: It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .
Journal ArticleDOI
Non-Linear Programming Via Penalty Functions
TL;DR: The algorithm presented in this paper solves the non-linear programming problem by transforming it into a sequence of unconstrained maximization problems and is shown to be a dual feasible method.
Journal ArticleDOI
Exact penalty functions in nonlinear programming
TL;DR: It is shown that the existence of a strict local minimum satisfying the constraint qualification of [16] or McCormick's second order sufficient optimality condition implies theexistence of a class of exact local penalty functions (that is ones with a finite value of the penalty parameter) for a nonlinear programming problem.