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A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration

Zainab Hassan Ahmed, Mohamed Hbaib, Khalil K. Abbo (2024)

Applications of Mathematics

The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can lead to subsequent poor directions and steps. To address this issue, we propose a modification to the FR method, and then we develop it into the three-term conjugate gradient method in this paper. The suggested methods, named ``HZF'' and ``THZF'', preserve the descent property of the FR method while mitigating the drawbacks. The algorithms incorporate...

A moving mesh fictitious domain approach for shape optimization problems

Raino A.E. Mäkinen, Tuomo Rossi, Jari Toivanen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A new numerical method based on fictitious domain methods for shape optimization problems governed by the Poisson equation is proposed. The basic idea is to combine the boundary variation technique, in which the mesh is moving during the optimization, and efficient fictitious domain preconditioning in the solution of the (adjoint) state equations. Neumann boundary value problems are solved using an algebraic fictitious domain method. A mixed formulation based on boundary Lagrange multipliers is...

A multidimensional singular stochastic control problem on a finite time horizon

Marcin Boryc, Łukasz Kruk (2015)

Annales UMCS, Mathematica

A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique

A multiscale correction method for local singular perturbations of the boundary

Marc Dambrine, Grégory Vial (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uE of a second order elliptic equation posed in the perturbed domain with respect to the size parameter ε of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of uE based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We...

A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors

Masahiro Inuiguchi (2006)

Kybernetika

In this paper, a necessity measure optimization model of linear programming problems with fuzzy oblique vectors is discussed. It is shown that the problems are reduced to linear fractional programming problems. Utilizing a special structure of the reduced problem, we propose a solution algorithm based on Bender’s decomposition. A numerical example is given.

A new approach to the constrained controllability problem

Ali Boutoulout, Layla Ezzahri, Hamid Bourray (2014)

Applicationes Mathematicae

We consider the problem of internal regional controllability with output constraints. It consists in steering a hyperbolic system to a final state between two prescribed functions only on a subregion of the evolution system domain. This problem is solved by characterizing the optimal control in terms of a subdifferential associated with the minimized functional.

A new method based on least-squares support vector regression for solving optimal control problems

Mitra Bolhassani, Hassan Dana Mazraeh, Kourosh Parand (2024)

Kybernetika

In this paper, a new application of the Least Squares Support Vector Regression (LS-SVR) with Legendre basis functions as mapping functions to a higher dimensional future space is considered for solving optimal control problems. At the final stage of LS-SVR, an optimization problem is formulated and solved using Maple optimization packages. The accuracy of the method are illustrated through numerical examples, including nonlinear optimal control problems. The results demonstrate that the proposed...

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