Duality for higher order variational control programming problems
01 Nov 2017-International Transactions in Operational Research (John Wiley & Sons, Ltd)-Vol. 24, Iss: 6, pp 1549-1560
TL;DR: The concept of higher order (F,G,ρ)-convex function for a continuous case for variational control problem is introduced and appropriate duality results are obtained using aforesaid assumptions.
About: This article is published in International Transactions in Operational Research.The article was published on 2017-11-01. It has received 8 citations till now. The article focuses on the topics: Weak duality & Strong duality.
Citations
More filters
01 Sep 1995
34 citations
TL;DR: This paper uses the exact l1 penalty function method to solve a multi-dimensional first-order PDE constrained control optimization problem and shows that an optimal solution is a minimizer of its associated penalized problem under the hypothesis of convex Lagrange functional.
19 citations
TL;DR: In this paper, the concept of invexity associated with multiple integral vector functionals is introduced and several results of duality for a class of multiobject objects are derived.
Abstract: In this paper, by using the recently introduced concept of invexity associated with multiple integral vector functionals, we introduce several results of duality for a class of multiobjecti...
15 citations
TL;DR: By using the notion of a Lagrangian function, the connection between a saddle-point in the modified objective function variational problem and an optimal solution in the considered Variational problem is presented.
7 citations
Abstract: In this paper, we focus our study on a multiobjective variational control problem and establish sufficient optimality conditions under the assumptions of α -V-univex function. Furthermore, mixed type duality results are also discussed under the aforesaid assumption in order to relate the primal and dual problems. Examples are given to show the existence of α -V-univex function and to elucidate duality result.
2 citations
References
More filters
TL;DR: A dual problem associated with a primal nonlinear programming problem is presented in this paper, where second derivatives of the functions constituting the primal problem are derived for this pair of problems, and duality results for these problems are also given.
225 citations
"Duality for higher order variationa..." refers background in this paper
...Introduction Higher order duality in nonlinear programming has been studied by several authors (Mangasarian, 1975; Mond and Weir, 1981–1983; Ahmad et al., 2007, 2013)....
[...]
TL;DR: For a multiobjective nonlinear program which involved inequality and equality constraints, Wolfe, Mond-Weir, and general MWE type duals are formulated and the concept of efficiency (Pareto optimum) is used to state some duality results under generalized (F, ϱ)-convexity assumptions as mentioned in this paper.
208 citations
77 citations
"Duality for higher order variationa..." refers background in this paper
...The concept of optimal control (Chinchuluun et al., 2009, 2010, 2013) with classical calculus of variation was first developed by Hanson (1964)....
[...]
01 Sep 2003
TL;DR: Anragradient Approach to the Solution of Two Person Non-Zero Sum Games, nonlinear Phenomena in Economics, and The Points of a Linear Manifold Nearest to a Given Vector are among the articles reviewed.
Abstract: Extragradient Approach to the Solution of Two Person Non-Zero Sum Games (A Antipin) Nonlinear Phenomena in Economics (S Budnyam) On Some Theory, Methods and Algorithms for Concave Programming (R Enkhbat) Maximum Clique Regularizations (D Fortin & I Tseveendorj) The Role of Optimization in Economics (D W Katzner) A Global Optimization Approach to Solving Equilibrium Programming Problems (O Khamisov) Comparison of Convex Relaxations for Monomials of Odd Degree (L Liberti) Structural Stability of Vector Optimization Problems (P Mbunga) Optimization for Black-Box Objective Functions (H Nakayama et al.) New Variants of Gradient Type Methods in Optimal Control Problems (V A Srochko) Controlled Systems with Distributed Parameters: Optimally Conditions and Optimization Methods in Class of Smooth Restricted Controls (O V Vasiliev) The Points of a Linear Manifold Nearest to a Given Vector (V I Zorkaltsev) and other articles.
64 citations
"Duality for higher order variationa..." refers background in this paper
...The concept of optimal control (Chinchuluun et al., 2009, 2010, 2013) with classical calculus of variation was first developed by Hanson (1964)....
[...]
01 Sep 1995
34 citations