On optimality conditions for interval optimisation problems using generalised Hukuhara difference and constrained interval arithmetic

2021 ◽  
Vol 19 (2) ◽  
pp. 204
Author(s):  
Shaveta Kumari ◽  
Saurabh Srivastava
Keyword(s):  
Optimality Conditions ◽  
Interval Arithmetic ◽  
Hukuhara Difference

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.

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.

Analysis of power pattern in CLAS with the material thickness and properties error through interval arithmetic

2017 ◽  
Vol 11 (10) ◽  
pp. 1354-1362 ◽  
Author(s):  
Peng Li ◽  
Witold Pedrycz ◽  
Wanye Xu ◽  
Li‐Wei Song
Keyword(s):  
Interval Arithmetic ◽  
Material Thickness ◽  
Power Pattern

scholarly journals Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

2021 ◽  
Vol 189 (1) ◽  
pp. 221-243
Author(s):  
Jiawei Chen ◽  
Suliman Al-Homidan ◽  
Qamrul Hasan Ansari ◽  
Jun Li ◽  
Yibing Lv
Keyword(s):  
Optimality Conditions ◽  
Fractional Programming ◽  
Uncertain Data ◽  
Necessary Optimality Conditions
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