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Deep Neural Network With a Smooth Monotonic Output Layer for Dynamic Risk Prediction. [PDF]
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Penalty functions with a small penalty parameter
Optimization Methods and Software, 2002In this article, we study the nonlinear penalization of a constrained optimization problem and show that the least exact penalty parameter of an equivalent parametric optimization problem can be diminished. We apply the theory of increasing positively homogeneous (IPH) functions so as to derive a simple formula for computing the least exact penalty ...
A.M. Rubinov, X.Q. Yang, A.M. Bagirov
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Exact Penalty Functions in Constrained Optimization
SIAM Journal on Control and Optimization, 1989Summary: Formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated, thus providing a unified framework for the study of both nondifferentiale and continuously differentiable penalty functions.
Di Pillo, G., Grippo, L.
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Linearization and Penalty Functions
Cybernetics and Systems Analysis, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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SIAM Journal on Optimization, 2003
A new approach to exact penalization of a constrained, nonlinear optimization problem is introduced. This is motivated by the desire to deal with the following list of perceived failures of other exact penalty methods: 1. nonsmoothness is avoided; 2. the penalized objective remains bounded below under mild assumptions; 3.
Huyer, Waltraud, Neumaier, Arnold
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A new approach to exact penalization of a constrained, nonlinear optimization problem is introduced. This is motivated by the desire to deal with the following list of perceived failures of other exact penalty methods: 1. nonsmoothness is avoided; 2. the penalized objective remains bounded below under mild assumptions; 3.
Huyer, Waltraud, Neumaier, Arnold
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IFAC Proceedings Volumes, 2000
Abstract Some Optimal Control problems can be reduce to problems of Nonlinear Progran1ming. Methods of penalty functions are widely used in Nonlinear Programming. Theorems of the existence of exact penalty parameters for solving of the problems of Nonlinear Programming by the method of exact penalty functions are proved.
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Abstract Some Optimal Control problems can be reduce to problems of Nonlinear Progran1ming. Methods of penalty functions are widely used in Nonlinear Programming. Theorems of the existence of exact penalty parameters for solving of the problems of Nonlinear Programming by the method of exact penalty functions are proved.
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An M-Objective Penalty Function Algorithm Under Big Penalty Parameters
Journal of Systems Science and Complexity, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zheng, Ying, Meng, Zhiqing, Shen, Rui
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2003
Recall that a relation ≥ defined on a set X is called pre-order if (i) x ≥ x, for all x ∈ X, and (ii) x ≥ y and y ≥ z imply x ≥z. If x ≥ y and y ≥ x, then x and y are called equivalent elements. A pre-order relation is called complete if, for any two elements x and y, either x ≥ y or y ≥ x.
Alexander Rubinov, Xiaoqi Yang
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Recall that a relation ≥ defined on a set X is called pre-order if (i) x ≥ x, for all x ∈ X, and (ii) x ≥ y and y ≥ z imply x ≥z. If x ≥ y and y ≥ x, then x and y are called equivalent elements. A pre-order relation is called complete if, for any two elements x and y, either x ≥ y or y ≥ x.
Alexander Rubinov, Xiaoqi Yang
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