Characterizations of Benson proper efficiency of set-valued optimization in real linear spaces

2019 ◽  
Vol 17 (1) ◽  
pp. 1168-1182
Author(s):  
Hongwei Liang ◽  
Zhongping Wan
Keyword(s):  
Optimization Problem ◽  
Saddle Points ◽  
Sufficient Conditions ◽  
Proper Efficiency ◽  
Solid Cone ◽  
Linear Spaces ◽  
New Class ◽  
Benson Proper Efficiency ◽  
Real Linear ◽  
Necessary And Sufficient

Abstract A new class of generalized convex set-valued maps termed relatively solid generalized cone-subconvexlike maps is introduced in real linear spaces not equipped with any topology. This class is a generalization of generalized cone-subconvexlike maps and relatively solid cone-subconvexlike maps. Necessary and sufficient conditions for Benson proper efficiency of set-valued optimization problem are established by means of scalarization, Lagrange multipliers, saddle points and duality. The results generalize and improve some corresponding ones in the literature. Some examples are afforded to illustrate our results.

scholarly journals ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhi-Ang Zhou
Keyword(s):  
Saddle Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Saddle Points ◽  
Linear Spaces ◽  
Equivalent Characterization ◽  
Generalized Cone Subconvexlikeness ◽  
Real Linear ◽  
The Relationship

We studyϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization ofϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between theϵ-Henig saddle point of the Lagrangian set-valued map and theϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.

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 Second-Order Optimality Conditions for Set-Valued Optimization Problems Under Benson Proper Efficiency

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Qilin Wang ◽  
Guolin Yu
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Second Order ◽  
Proper Efficiency ◽  
Second Order Optimality Conditions ◽  
Benson Proper Efficiency ◽  
Necessary And Sufficient ◽  
Proper Efficient Solutions

Some new properties are obtained for generalized second-order contingent (adjacent) epiderivatives of set-valued maps. By employing the generalized second-order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set-valued optimization problems. The results obtained improve the corresponding results in the literature.

Twisted Sasakian Metric on the Tangent Bundle and Harmonicity

2021 ◽  
Vol 62 ◽  
pp. 53-66
Author(s):  
Fethi Latti ◽  
◽  
Hichem Elhendi ◽  
Lakehal Belarbi
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Harmonic Vector ◽  
New Class ◽  
Necessary And Sufficient ◽  
Sasakian Metric ◽  
Harmonic Vector Fields

In the present paper, we introduce a new class of natural metrics on the tangent bundle $TM$ of the Riemannian manifold $(M,g)$ denoted by $G^{f,h}$ which is named a twisted Sasakian metric. A necessary and sufficient conditions under which a vector field is harmonic with respect to the twisted Sasakian metric are established. Some examples of harmonic vector fields are presented as well.

scholarly journals On a topology between Tα and Tγα

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3209-3221
Author(s):  
Dimitrije Andrijevic
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Closure Operators ◽  
New Class ◽  
Necessary And Sufficient

Using the topology T in a topological space (X,T), a new class of generalized open sets called ?-preopen sets, is introduced and studied. This class generates a new topology Tg which is larger than T? and smaller than T??. By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for Tg to coincide with T? , T? or T??.

Further results for Gauss-Poisson processes

1972 ◽  
Vol 4 (01) ◽  
pp. 151-176 ◽  
Author(s):  
R. K. Milne ◽  
M. Westcott
Keyword(s):  
Point Processes ◽  
Sufficient Conditions ◽  
Infinite Divisibility ◽  
Poisson Processes ◽  
Generating Functional ◽  
Basic Approach ◽  
New Class ◽  
Two Measures ◽  
Necessary And Sufficient ◽  
Statistical Results

Newman (1970) introduced an interesting new class of point processes which he called Gauss-Poisson. They are characterized, in the most general case, by two measures. We determine necessary and sufficient conditions on these measures for the resulting point process to be well defined, and proceed to a systematic study of its properties. These include stationarity, ergodicity, and infinite divisibility. We mention connections with other classes of point processes and some statistical results. Our basic approach is through the probability generating functional of the process.

scholarly journals Linear-quadratic optimization and some general hypotheses on optimal control

1999 ◽  
Vol 5 (4) ◽  
pp. 275-289 ◽  
Author(s):  
L. I. Rozonoer
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Quadratic Optimization ◽  
Necessary And Sufficient Conditions ◽  
Maximum Condition ◽  
Linear Quadratic ◽  
Existence Of Optimal Control ◽  
Necessary And Sufficient

Necessary and sufficient conditions for existence of optimal control for all initial data are proved forLQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.

scholarly journals Positivity and stabilization of fractional 2D linear systems described by the Roesser model

2010 ◽  
Vol 20 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Krzysztof Rogowski
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Roesser Model ◽  
Fractional Difference ◽  
Fractional Systems ◽  
New Class ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Positivity and stabilization of fractional 2D linear systems described by the Roesser modelA new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2DZ-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.

Sign in / Sign up

Export Citation Format

Share Document