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Exact Regularization of Convex Programs
SIAM Journal on Optimization, 2008The regularization of a convex program is exact if all solutions of the regularized problem are also solutions of the original problem for all values of the regularization parameter below some positive threshold. For a general convex program, we show that the regularization is exact if and only if a certain selection problem has a Lagrange multiplier ...
Michael P. Friedlander, Paul Tseng
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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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Convex infinite horizon programs
Mathematical Programming, 1983We establish conditions under which a sequence of finite horizon convex programs monotonically increases in value to the value of the infinite program; a subsequence of optimal solutions converges to the optimal solution of the infinite problem. If the conditions we impose fail, then (roughtly) the optimal value of the infinite horizon problem is an ...
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A Convergent Procedure for Convex Programming
Journal of the Society for Industrial and Applied Mathematics, 1963Gegeben ist eine beliebige Menge \(X\) und ein Vektor \(v(x) = (v_0(x), v_1(x),\dots, v_m(x))\), dessen Komponenten auf \(X\) definierte reellwertige Funktionen sind. Ferner werden definiert: \(u\cdot v\) als Skalarprodukt der Vektoren \(u = (u_0, u_1,\dots, u_m)\) and \(v = (v_0, v_1,\dots, v_m)\), der Wertebereich von \(v(x)\) als \(V = \{v(x)\mid x ...
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Convex Programming and Optimal Control
Journal of the Society for Industrial and Applied Mathematics Series A Control, 1965The use of convex programming to attack problems of optimal control is not new, but it is becoming of increasing interest. Techniques of steepest descent and gradient projection have been used by Balakrishnan [1], Goldstein [2], [3], Neustadt [4], and Neustadt and Paiewonsky [5].
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Preliminaries: Convex Analysis and Convex Programming
2001In this chapter, we give some definitions and results connected with convex analysis, convex programming, and Lagrangian duality. In Part Two, these concepts and results are utilized in developing suitable optimality conditions and numerical methods for solving some convex problems.
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From Convex to Mixed Programming
1985This paper is concerned with convex programming, differential programming and mixed programming. All spaces involved will assumed to be linear, normed and complete, so that we limit ourselves to Banach spaces, although in a number of cases locally convex topological vector spaces would do as well.
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