shape-measure method for solving elliptic optimal shape problems (fixed control case)

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Control/fictitious domain method for solving optimal shape design problems

— Combining a fictitious domain and an optimal control approach, we present a new method for the numerical realization of optimal shape design problems. This approach enables us to perform ail calculations on a fixed domain with a fixed grid. Finite element approximation is studied. Résumé. — On présente une méthode nouvelle pour la résolution numérique des problèmes de Voptimisation de la form...

A Method for Solving Optimal Control Problems Using Genetic Programming

This paper deals with a novel method for solving optimal control problems based on genetic programming. This approach produces some trial solutions and seeks the best of them. If the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. Using numerical examples, we will demonstrate how to use the results.

Optimal Shape for Elliptic Problems with Random Perturbations

In this paper we analyze the relaxed form of a shape optimization problem with state equation { − div ( a(x)Du ) = f in D boundary conditions on ∂D. The new fact is that the term f is only known up to a random perturbation ξ(x, ω). The goal is to find an optimal coefficient a(x), fulfilling the usual constraints α ≤ a ≤ β and ∫ D a(x) dx ≤ m, which minimizes a cost function of the form

Solving The Optimal Control Problems Using Homotopy Perturbation Transform Method

Inthispaper,wesolveHamilton-Jocobi-Bellman(HJB)equationsarisinginoptimalcontrolproblems usingHomotopyPerturbationTransformMethod(HPTM).Theproposedmethodisacombinedform oftheLaplaceTransformationMethodwiththeHomotopyPerturbationMethodtoproduceahighly effectivemethodtohandlemanyproblems. ApplyingtheHPTM,solutionprocedurebecomeseasier, simplerandmorestraightforward. Someillustrativeexamplesaregive...

Generalized B-spline functions ‎method‎‎ for solving optimal control problems

‎In this paper we introduce a numerical approach that solves optimal control problems (OCPs) ‎using collocation methods‎. ‎This approach is based upon B-spline functions‎. ‎The derivative matrices between any two families of B-spline functions are utilized to‎ ‎reduce the solution of OCPs to the solution of nonlinear optimization problems‎. ‎Numerical experiments confirm our heoretical findings‎.