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Journal of the Society for Industrial and Applied Mathematics, 1963
Introduction. In their paper, Newton's Method for Convex Programming and Tchebycheff Approximation [1], E. WV. Cheney and A. A. Goldstein consider the following problem: "Given a convex continuous function F defined on a closed convex subset K of En, obtain (if such exists) a point x of K such that F(x) ?
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Introduction. In their paper, Newton's Method for Convex Programming and Tchebycheff Approximation [1], E. WV. Cheney and A. A. Goldstein consider the following problem: "Given a convex continuous function F defined on a closed convex subset K of En, obtain (if such exists) a point x of K such that F(x) ?
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Mathematical Programming, 1978
A piecewise convex program is a convex program such that the constraint set can be decomposed in a finite number of closed convex sets, called the cells of the decomposition, and such that on each of these cells the objective function can be described by a continuously differentiable convex function.
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A piecewise convex program is a convex program such that the constraint set can be decomposed in a finite number of closed convex sets, called the cells of the decomposition, and such that on each of these cells the objective function can be described by a continuously differentiable convex function.
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Variant of nontandard convex programming
Siberian Mathematical Journal, 1986Rules for computing subdifferentials of convex operators with infinitesimal accuracy are derived. Applications to convex minimization problems are considered. The exposition is based on internal set theory, invented by \textit{E. Nelson} [Bull. Am. Math. Soc. 83, 1165-1198 (1977; Zbl 0373.02040)].
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A Duality Theorem for Convex Programs
IBM Journal of Research and Development, 1960A proof is given for a duality theorem for a class of convex programs, i.e., constrained minimization of convex functions. A simple example is included.
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Convex Quadratic Programming Approach
Journal of Global Optimization, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Convex Sets and Convex Programming
1981In this chapter we concentrate on properties of convex sets in a Hilbert space and some of the related problems of importance in application to convex programming: variational problems for convex functions over convex sets, central to which are the Kuhn-Tucker theorem and the minimax theorem of von Neumann, which in turn are based on the “separation ...
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Surrogate Programming and Multipliers in Quasi-convex Programming
SIAM Journal on Control and Optimization, 2004Summary: A result due to \textit{D. G. Luenberger} [SIAM J. Appl. Math. 16, 1090--1095 (1968; Zbl 0212.23905)] on the existence of multipliers in a quasi-convex programming problem is extended to the case of constraints given by an arbitrary convex cone under a constraint qualification condition more general than Slater's condition.
Jean-Paul Penot, Michel Volle
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Dynamic programming and convex clustering
Algorithmica, 1994A dynamic programming procedure is developed for \(k\)-clustering problems for linear ordered sets. If the problem has an optimal solution which is convex (which implies that the cluster sets are intervals) then the dynamic programming approach gives an \(O(kn^ 3)\)-algorithm where \(n\) is the number of items.
Vladimir Batagelj +2 more
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Convex Programming by Tangential Approximation
Management Science, 1963This paper describes an algorithm for the solution of the convex programming problem using the simplex method. The algorithm is computationally very simple, requiring the solution of a single linear programming problem which can be accomplished with only slight modification of existing computer codes for the revised simplex method.
H. O. Hartley, R. R. Hocking
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Conjugacy in quasi-convex programming
Mathematical Programming, 1984One introduces a conjugacy relation and a subdifferential on the class of functions \(g:R^ n\to\bar R.\) It is shown that \(g^{**}=g\) iff g is proper (i.e. \(g(0)=\sup g),\) homogeneous of degree zero and evenly quasi- convex. As noted by the authors, the above notions are much related to the ones introduced by \textit{J. P. Crouzeix} [Math. Oper. Res.
Ury Passy, Eliezer Z. Prisman
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