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Exact penalty functions in nonlinear programming

Mathematical Programming, 1979
It is shown that the existence of a strict local minimum satisfying the constraint qualification of [16] or McCormick's [12] second order sufficient optimality condition implies the existence of a class of exact local penalty functions (that is ones with a finite value of the penalty parameter) for a nonlinear programming problem.
Shih-Ping Han, Olvi L. Mangasarian
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A Continuously Differentiable Exact Penalty Function for Nonlinear Programming Problems with Inequality Constraints [PDF]

SIAM Journal on Control and Optimization, 1985
In this paper it is shown that, given a nonlinear programming problem with inequality constraints, it is possible to construct a continuously differentiable exact penalty function whose global or local unconstrained minimizers correspond to global or ...
G Di Pillo, L Grippo
exaly   +2 more sources

On differentiable exact penalty functions

Journal of Optimization Theory and Applications, 1986
We study a differentiable exact penalty function for solving twice continuously differentiable inequality constrained optimization problems. Under certain assumptions on the parameters of the penalty function, we show the equivalence of the stationary points of this function and the Kuhn-Tucker points of the restricted problem as well as their extreme ...
Vinante, C., Pintos, S.
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Optimality Conditions via Exact Penalty Functions

SIAM Journal on Optimization, 2010
In this paper, we study KKT optimality conditions for constrained nonlinear programming problems and strong and Mordukhovich stationarities for mathematical programs with complementarity constraints using $l_p$ penalty functions, with $0\leq p\leq1$. We introduce some optimality indication sets by using contingent derivatives of penalty function terms.
Meng, K, Yang, XQ
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Smoothing Partially Exact Penalty Function of Biconvex Programming

Asia-Pacific Journal of Operational Research, 2020
In this paper, a smoothing partial exact penalty function of biconvex programming is studied. First, concepts of partial KKT point, partial optimum point, partial KKT condition, partial Slater constraint qualification and partial exactness are defined for biconvex programming.
Rui Shen 0001, Zhiqing Meng, Min Jiang
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An exact penalty function for semi-infinite programming

Mathematical Programming, 1987
The authors describe an exact penalty function for nonlinear semi- infinite programming. This function is a generalization of the \(\ell_ 1\) exact penalty function for nonlinear programming and may be used as a merit function for semi-infinite programming methods.
Andrew R. Conn, Nicholas I. M. Gould
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A sufficient condition for exact penalty functions

Optimization Letters, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An exact penalty function based on the projection matrix

Applied Mathematics and Computation, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ricardo Luiz Utsch de Freitas Pinto, Ricardo Poley Martins Ferreira   +1 more
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Exact Penalty Functions for Nondifferentiable Programming Problems

1989
In recent years an increasing attention has been devoted to the use of nondifferentiable exact penalty functions for the solution of nonlinear programming problems. However, as pointed out in [22], virtually all the published literature on exact penalty functions treats one of two cases: either the nonlinear programming problem is a convex problem (see,
DI PILLO, Gianni, FACCHINEI, Francisco
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Smoothing Approximation to the New Exact Penalty Function with Two Parameters

Asia-Pacific Journal of Operational Research, 2021
In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem.
Jing Qiu, Jiguo Yu, Shujun Lian
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