scholarly journals Optimality conditions for linear copositive programming problems with isolated immobile indices

Optimization ◽  
2018 ◽  
Vol 69 (1) ◽  
pp. 145-164 ◽  
Author(s):  
O. I. Kostyukova ◽  
T. V. Tchemisova
Keyword(s):  
Optimality Conditions ◽  
Copositive Programming

scholarly journals Generalized problem of linear copositive programming

2019 ◽  
Vol 55 (3) ◽  
pp. 299-308
Author(s):  
O. I. Kostyukova ◽  
T. V. Tchemisova
Keyword(s):  
Finite Number ◽  
Objective Function ◽  
Optimality Conditions ◽  
Special Class ◽  
Optimization Problems ◽  
Decision Variable ◽  
Copositive Programming ◽  
Feasible Sets

We consider a special class of optimization problems where the objective function is linear w.r.t. decision variable х and the constraints are linear w.r.t. х and quadratic w.r.t. index t defined in a given cone. The problems of this class can be considered as a generalization of semi-definite and copositive programming problems. For these problems, we formulate an equivalent semi-infinite problem and define a set of immobile indices that is either empty or a union of a finite number of convex bounded polyhedra. We have studied properties of the feasible sets of the problems under consideration and use them to obtain new efficient optimality conditions for generalized copositive problems. These conditions are CQ-free and have the form of criteria.

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.

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.

Nondegeneracy of optimality conditions in control problems for a radiative–conductive heat transfer model

2016 ◽  
Vol 289 ◽  
pp. 371-380 ◽  
Author(s):  
Alexander Yu. Chebotarev ◽  
Andrey E. Kovtanyuk ◽  
Gleb V. Grenkin ◽  
Nikolai D. Botkin ◽  
Karl-Heinz Hoffmann
Keyword(s):  
Heat Transfer ◽  
Optimality Conditions ◽  
Heat Transfer Model ◽  
Conductive Heat Transfer ◽  
Control Problems ◽  
Transfer Model ◽  
Conductive Heat
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