On optimal singular control problem for general Mckean-Vlasov differential equations: Necessary and sufficient optimality conditions

2018 ◽  
Vol 39 (3) ◽  
pp. 1202-1219 ◽  
Author(s):  
Mokhtar Hafayed ◽  
Shahlar Meherrem ◽  
Şaban Eren ◽  
Deniz Hasan Guçoglu
Keyword(s):  
Differential Equations ◽  
Control Problem ◽  
Optimality Conditions ◽  
Singular Control ◽  
Sufficient Optimality Conditions ◽  
Singular Control Problem ◽  
Necessary And Sufficient

scholarly journals A note on the paper "Necessary and sufficient optimality conditions using convexifactors for mathematical programs with equilibrium constraints"

2021 ◽  
Author(s):  
Nazih Abderrazzak Gadhi
Keyword(s):  
Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Equilibrium Constraints ◽  
Mathematical Programs ◽  
Necessary And Sufficient

In this work, some counterexamples are given to refute some results in the paper by Kohli (RAIRO-Oper. Res. 53, 1617-1632, 2019). We correct the faulty in some of his results.

scholarly journals Strict lower subdifferentiability and applications

1999 ◽  
Vol 40 (3) ◽  
pp. 379-391 ◽  
Author(s):  
H. Xu ◽  
A. M. Rubinov ◽  
B. M. Glover
Keyword(s):  
Global Convergence ◽  
Optimality Conditions ◽  
Convex Subset ◽  
Sufficient Optimality Conditions ◽  
Descent Direction ◽  
Minimization Problems ◽  
Convergence Results ◽  
Lower Subdifferential ◽  
Necessary And Sufficient ◽  
Convex Subdifferential

AbstractWe investigate the strict lower subdifferentiability of a real-valued function on a closed convex subset of Rn. Relations between the strict lower subdifferential, lower subdifferential, and the usual convex subdifferential are established. Furthermore, we present necessary and sufficient optimality conditions for a class of quasiconvex minimization problems in terms of lower and strict lower subdifferentials. Finally, a descent direction method is proposed and global convergence results of the consequent algorithm are obtained.

scholarly journals Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 12 ◽  
Author(s):  
Xiangkai Sun ◽  
Hongyong Fu ◽  
Jing Zeng
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Sufficient Optimality Conditions ◽  
Convex Constraint ◽  
Approximate Optimality Conditions ◽  
Necessary And Sufficient

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.

scholarly journals Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhen Wu ◽  
Feng Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Linear Quadratic ◽  
Regular Control

We consider a stochastic recursive optimal control problem in which the control variable has two components: the regular control and the impulse control. The control variable does not enter the diffusion coefficient, and the domain of the regular controls is not necessarily convex. We establish necessary optimality conditions, of the Pontryagin maximum principle type, for this stochastic optimal control problem. Sufficient optimality conditions are also given. The optimal control is obtained for an example of linear quadratic optimization problem to illustrate the applications of the theoretical results.

scholarly journals Duality and Lagrange multipliers for nonsmooth multiobjective programming

2006 ◽  
Vol 74 (3) ◽  
pp. 369-383 ◽  
Author(s):  
Houchun Zhou ◽  
Wenyu Sun
Keyword(s):  
Optimality Conditions ◽  
Lagrange Multipliers ◽  
Constraint Qualification ◽  
Multiobjective Programming ◽  
Sufficient Optimality Conditions ◽  
Dual Model ◽  
Mixed Duality ◽  
Nonsmooth Multiobjective Programming ◽  
Necessary And Sufficient ◽  
Dual Models

Without any constraint qualification, the necessary and sufficient optimality conditions are established in this paper for nonsmooth multiobjective programming involving generalised convex functions. With these optimality conditions, a mixed dual model is constructed which unifies two dual models. Several theorems on mixed duality and Lagrange multipliers are established in this paper.

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