Duality relations and optimality conditions in linear stochastic programming

Cybernetics ◽  
1987 ◽  
Vol 23 (1) ◽  
pp. 128-135
Author(s):  
A. I. Yastremskii
Keyword(s):  
Stochastic Programming ◽  
Optimality Conditions ◽  
Duality Relations

Necessary optimality conditions for two-stage stochastic programming problems

Optimization ◽  
1985 ◽  
Vol 16 (4) ◽  
pp. 607-616 ◽  
Author(s):  
Silvia Vogel
Keyword(s):  
Stochastic Programming ◽  
Optimality Conditions ◽  
Necessary Optimality Conditions ◽  
Two Stage

scholarly journals Karush-Kuhn-Tucker optimality conditions and duality for multiobjective semi-infinite programming with equilibrium constraints

2020 ◽  
pp. 24-24
Author(s):  
Thanh Le
Keyword(s):  
Optimality Conditions ◽  
Equilibrium Constraints ◽  
Dual Problems ◽  
Duality Relations ◽  
Infinite Programming ◽  
Convexity Assumptions ◽  
Necessary And Sufficient

The purpose of this paper is to study multiobjective semi-infinite programming with equilibrium constraints. Firstly, the necessary and sufficient Karush-Kuhn-Tucker optimality conditions for multiobjective semi-infinite programming with equilibrium constraints are established. Then, we formulate types of Wolfe and Mond-Weir dual problems and investigate duality relations under convexity assumptions. Some examples are given to verify our results.

Optimality conditions in stochastic programming

Cybernetics ◽  
1980 ◽  
Vol 16 (1) ◽  
pp. 154-158 ◽  
Author(s):  
A. I. Yastremskii
Keyword(s):  
Stochastic Programming ◽  
Optimality Conditions

Stochastic Programming Problems with Probability and Quantile Functions

1997 ◽  
Vol 48 (8) ◽  
pp. 849-849
Author(s):  
A I Kibzun ◽  
Y S Kan
Keyword(s):  
Stochastic Programming ◽  
Quantile Functions

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Nonlinear Stochastic Programming Involving CVaR in the Objective and Constraints

Informatica ◽  
2015 ◽  
Vol 26 (4) ◽  
pp. 569-591 ◽  
Author(s):  
Valerijonas Dumskis ◽  
Leonidas Sakalauskas
Keyword(s):  
Stochastic Programming

Generalized Fixed-Structure Optimality Conditions for H2 Optimal Control

1993 ◽  
Author(s):  
Emmanuel G. Collins ◽  
Wassim M. Haddad ◽  
Sidney S. Ying
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Fixed Structure

Analysis and design of thermo-mechanical interfaces

2012 ◽  
Vol 60 (2) ◽  
pp. 205-213
Author(s):  
K. Dems ◽  
Z. Mróz
Keyword(s):  
Optimality Conditions ◽  
Mechanical Loading ◽  
Material Properties ◽  
Structural Response ◽  
External Boundary ◽  
Mechanical Loads ◽  
Internal Interface ◽  
Analysis And Design ◽  
First Order ◽  
Mechanical Nature

Abstract. An elastic structure subjected to thermal and mechanical loading with prescribed external boundary and varying internal interface is considered. The different thermal and mechanical nature of this interface is discussed, since the interface form and its properties affect strongly the structural response. The first-order sensitivities of an arbitrary thermal and mechanical behavioral functional with respect to shape and material properties of the interface are derived using the direct or adjoint approaches. Next the relevant optimality conditions are formulated. Some examples illustrate the applicability of proposed approach to control the structural response due to applied thermal and mechanical loads.

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