scholarly journals Set Intersection Theorems and Existence of Optimal Solutions

2006 ◽  
Vol 110 (2) ◽  
pp. 287-314 ◽  
Author(s):  
Dimitri P. Bertsekas ◽  
Paul Tseng
Keyword(s):  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Set Intersection

scholarly journals Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 569
Author(s):  
Wu
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Optimal Solutions ◽  
Membership Functions ◽  
Fuzzy Decision ◽  
Existence Of Optimal Solutions ◽  
Decision Variables ◽  
Linear Programming Problems

The numerical method for solving the fuzzy linear programming problems with fuzzydecision variables is proposed in this paper. The difficulty for solving this kind of problem is thatthe decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative realnumbers. In other words, the decision variables are assumed to be membership functions. One of thepurposes of this paper is to derive the analytic formula of error estimation regarding the approximateoptimal solution. On the other hand, the existence of optimal solutions is also studied in this paper.Finally we present two numerical examples to demonstrate the usefulness of the numerical method.

scholarly journals Optimal control of nonlinear second order evolution equations

1993 ◽  
Vol 6 (2) ◽  
pp. 123-135 ◽  
Author(s):  
N. U. Ahmed ◽  
Sebti Kerbal
Keyword(s):  
Optimal Control ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Lagrange Problem

In this paper we study the optimal control of systems governed by second order nonlinear evolution equations. We establish the existence of optimal solutions for Lagrange problem.

scholarly journals Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xilu Wang ◽  
Xiaoliang Cheng
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Weak Form ◽  
Constitutive Law ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
External Forces ◽  
Weak Topologies

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

Optimal control of static contact in finite strain elasticity

2020 ◽  
Vol 26 ◽  
pp. 95
Author(s):  
Anton Schiela ◽  
Matthias Stoecklein
Keyword(s):  
Optimal Control ◽  
Finite Strain ◽  
Path Following ◽  
Contact Problems ◽  
Finite Deformations ◽  
Elastic Contact ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Static Contact ◽  
Convergence Of Sequences

We consider the optimal control of elastic contact problems in the regime of finite deformations. We derive a result on existence of optimal solutions and propose a regularization of the contact constraints by a penalty formulation. Subsequential convergence of sequences of solutions of the regularized problem to original solutions is studied. Based on these results, a numerical path-following scheme is constructed and its performance is tested.

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