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  1. 2 Acta Physica Polonica A

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  1. 2 2017

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  1. 2 Evirgen F.

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Solution of a Class of Optimization Problems Based on Hyperbolic Penalty Dynamic Framework

100%
Evirgen F.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 3
1062-1065
EN
In this study, a gradient-based dynamic system is constructed in order to solve a certain class of optimization problems. For this purpose, the hyperbolic penalty function is used. Firstly, the constrained optimization problem is replaced with an equivalent unconstrained optimization problem via the hyperbolic penalty function. Thereafter, the nonlinear dynamic model is defined by using the derivative of the unconstrained optimization problem with respect to decision variables. To solve the resulting differential system, a steepest descent search technique is used. Finally, some numerical examples are presented for illustrating the performance of the nonlinear hyperbolic penalty dynamic system.
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Conformable Fractional Gradient Based Dynamic System for Constrained Optimization Problem

100%
Evirgen F.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 3
1066-1069
EN
A conformable fractional gradient based dynamic system with a steepest descent direction is proposed in this paper for a class of nonlinear programming problems. The solutions of the dynamic system, modelled with the conformable fractional derivative are investigated to obtain the minimizing point of the optimization problem. For this purpose, we use a step variational iteration method, adapted to use a conformable integral definition. Numerical simulations and comparisons show that the conformable fractional gradient based dynamic system is both feasible and efficient for a certain class of equality constrained optimization problems. Furthermore, the step variational iteration method, combined with the conformable integral definition, is a reliable tool for solving a system of fractional differential equations.
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