On the Triality Theory for a Quartic Polynomial Optimization Problem [PDF]
, 2011 This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003.
A. Jaffe +13 more
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Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems [PDF]
, 2010 In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave.
Bian, Baojun, Miao, Sheng, Zheng, Harry
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ON NECESSARY CONDITIONS FOR EFFICIENCY IN DIRECTIONALLY DIFFERENTIABLE OPTIMIZATION PROBLEMS [PDF]
This paper deals with multiobjective programming problems with in- equality, equality and set constraints involving Dini or Hadamard differentiable func- tions.
Do Van Luu, Manh-Hung Nguyen
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A Note on the Convergence of ADMM for Linearly Constrained Convex Optimization Problems
, 2016 This note serves two purposes. Firstly, we construct a counterexample to show that the statement on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex optimization problems in a highly ...
Chen, Liang, Sun, Defeng, Toh, Kim-Chuan
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Gronwall-type integral inequalities with impulses on time scales
Advances in Difference Equations, 2011 In this article, some Gronwall-type integral inequalities with impulses on time scales are investigated. Our results extend some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete ...
Kang Ying +4 more
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Non-differentiable multiobjective mixed symmetric duality under generalized convexity
Journal of Inequalities and Applications, 2011 The objective of this paper is to obtain a mixed symmetric dual model for a class of non-differentiable multiobjective nonlinear programming problems where each of the objective functions contains a pair of support functions.
Li Jueyou, Gao Ying
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Geometric Duality for Convex Vector Optimization Problems [PDF]
, 2011 Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space.
Heyde, Frank
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The Computational Complexity of Duality
, 2016 We show that for any given norm ball or proper cone, weak membership in its dual ball or dual cone is polynomial-time reducible to weak membership in the given ball or cone.
Friedland, Shmuel, Lim, Lek-Heng
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Duality in nondifferentiable minimax fractional programming with
Journal of Inequalities and Applications, 2011 In this article, we are concerned with a nondifferentiable minimax fractional programming problem. We derive the sufficient condition for an optimal solution to the problem and then establish weak, strong, and strict converse duality theorems for the ...
Kailey N +3 more
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On
Fixed Point Theory and Applications, 2011 A multiobjective fractional optimization problem (MFP), which consists of more than two fractional objective functions with convex numerator functions and convex denominator functions, finitely many convex constraint functions, and a geometric constraint
Kim Gwi, Lee Gue, Kim Moon
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