scholarly journals Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives

2021 ◽  
Author(s):  
Tung Nguyen
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
Second Order ◽  
Set Valued Mapping ◽  
Contingent Epiderivative ◽  
Wolfe Duality ◽  
Order Constraint ◽  
Sufficient Conditions For Optimality ◽  
Second Order Necessary Conditions

We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, as well as relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient  conditions for optimality of the Karush-Kuhn-Tucker type are established under the second-order constraint qualification. An application to Mond-Weir and Wolfe duality schemes is also presented. Some remarks and examples are provided to illustrate our results.

NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION

2014 ◽  
Vol 20 (3) ◽  
pp. 667-684 ◽  
Author(s):  
A. Kerem Coşar ◽  
Edward J. Green
Keyword(s):  
Optimization Problems ◽  
Infinite Horizon ◽  
Sufficient Conditions ◽  
Transversality Condition ◽  
Necessary And Sufficient Conditions ◽  
Infinite Horizon Optimization ◽  
Sufficient Conditions For Optimality ◽  
The Government ◽  
Duality Approach ◽  
Necessary And Sufficient

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

scholarly journals Minimization of nonsmooth integral functionals

1992 ◽  
Vol 15 (4) ◽  
pp. 673-679
Author(s):  
Nikolaos S. Papageorgiou ◽  
Apostolos S. Papageorgiou
Keyword(s):  
Sobolev Spaces ◽  
Convex Analysis ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Integral Functionals ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

In this paper we examine optimization problems involving multidimensional nonsmooth integral functionals defined on Sobolev spaces. We obtain necessary and sufficient conditions for optimality in convex, finite dimensional problems using techniques from convex analysis and in nonconvex, finite dimensional problems, using the subdifferential of Clarke. We also consider problems with infinite dimensional state space and we finally present two examples.

scholarly journals On G-invexity-type nonlinear programming problems

2015 ◽  
Vol 5 (1) ◽  
pp. 13-20
Author(s):  
Tadeusz Antczak ◽  
Manuel Arana Jiménez
Keyword(s):  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
Extremum Problem ◽  
Sufficient Optimality Conditions ◽  
New Class ◽  
Necessary And Sufficient ◽  
Wolfe Dual

In this paper, we introduce the concepts of KT-G-invexity and WD$-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable optimization problems. Further, the so-called G-Wolfe dual problem is defined for the considered extremum problem with inequality constraints. Under WD-G-invexity assumption, the necessary and sufficient conditions for weak duality between the primal optimization problem and its G-Wolfe dual problem are also established.

scholarly journals The optimality principle for second-order discrete and discrete-approximate inclusions

2021 ◽  
Vol 11 (2) ◽  
pp. 206-215
Author(s):  
Sevilay Demir Sağlam
Keyword(s):  
Differential Inclusions ◽  
Sufficient Conditions ◽  
Approximation Problem ◽  
Second Order ◽  
Equivalence Relations ◽  
Transversality Conditions ◽  
Mayer Problem ◽  
Set Valued Mapping ◽  
Nonlinear Inequality ◽  
Equivalence Theorems

This paper deals with the necessary and sufficient conditions of optimality for the Mayer problem of second-order discrete and discrete-approximate inclusions. The main problem is to establish the approximation of second-order viability problems for differential inclusions with endpoint constraints. Thus, as a supplementary problem, we study the discrete approximation problem and give the optimality conditions incorporating the Euler-Lagrange inclusions and distinctive transversality conditions. Locally adjoint mappings (LAM) and equivalence theorems are the fundamental principles of achieving these optimal conditions, one of the most characteristic properties of such approaches with second-order differential inclusions that are specific to the existence of LAMs equivalence relations. Also, a discrete linear model and an example of second-order discrete inclusions in which a set-valued mapping is described by a nonlinear inequality show the applications of these results.

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