Shape optimization of structures with pointwise state constraints

2005 ◽  
pp. 255-264 ◽  
Author(s):  
B. Rousselet
Keyword(s):  
Shape Optimization ◽  
State Constraints ◽  
Pointwise State Constraints

On the regularization of classical optimality conditions in a convex optimal control problem with state constraints

2020 ◽  
pp. 263-273
Author(s):  
Fedor A. Kuterin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
State Constraints ◽  
Lagrange Principle ◽  
Strongly Convex ◽  
Pointwise State Constraints ◽  
Integrable Functions ◽  
Square Integrable Functions

We consider the regularization of classical optimality conditions in a convex optimal control problem for a linear system of ordinary differential equations with pointwise state constraints such as equality and inequality, understood as constraints in the Hilbert space of square-integrable functions. The set of admissible task controls is traditionally embedded in the space of square-integrable functions. However, the target functional of the optimization problem is not, generally speaking, strongly convex. Obtaining regularized classical optimality conditions is based on a technique involving the use of two regularization parameters. One of them is used for the regularization of the dual problem, while the other is contained in a strongly convex regularizing addition to the target functional of the original problem. The main purpose of the obtained regularized Lagrange principle and the Pontryagin maximum principle is the stable generation of minimizing approximate solutions in the sense of J. Varga for the purpose of practical solving the considered optimal control problem with pointwise state constraints.

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