Abstract
In this paper, we consider an approximate analytical method of optimal homotopy asymptotic method-least square (OHAM-LS) to obtain a solution of nonlinear fractional-order gradient-based dynamic system (FOGBDS) generated from nonlinear programming (NLP) optimization problems. The problem is formulated in a class of nonlinear fractional differential equations, (FDEs) and the solutions of the equations, modelled with a conformable fractional derivative (CFD) of the steepest descent approach, are considered to find the minimizing point of the problem. The formulation extends the integer solution of optimization problems to an arbitrary-order solution. We exhibit that OHAM-LS enables us to determine the convergence domain of the series solution obtained by initiating convergence-control parameter Cj′s. Three illustrative examples were included to show the effectiveness and importance of the proposed techniques.
Highlights
Consider a nonlinear programming-constrained optimization problems (NLPCOPs) of the form min x∈Rn f ðxÞ subject to gkðxÞ ≤ and hkðxÞ = 0∀k ∈I f1, 2::mg, ð1Þ where f : Rn ⟶ R, hk : Rn ⟶ R, and gk : Rn ⟶ R, k, are C2 functions
In this paper, we showed that the steady-state solutions xðtÞ of the proposed system can be approximated analytically to the expected exact optimal solution x∗ of the nonlinear programming constrained optimization problem by optimal homotopy asymptotic method-least square (OHAM-LS) as t ⟶ ∞
Three examples are presented to illustrate the efficiency of the new method for solving NLPCOPs
Summary
Consider a nonlinear programming-constrained optimization problems (NLPCOPs) of the form min x∈Rn f ðxÞ subject to gkðxÞ. The usefulness of an arbitrary-order started receiving tremendous attention of researchers in the field of applied science and engineering in the last two decades where some authors in the area of optimization focused on developing approximate analytical methods for different types of nonlinear constrained optimization problems in the form of IVPs of nonlinear FDE systems including multistage ADM for NLP [24], a fractional dynamics trajectory approach [25], the convergence of HAM and application [26], fractional steepest descent approach [27], studied optimal solution of fractional gradient [28], gradient descent direction with Caputo derivative sense for BP neural networks [29], fractional-order gradient methods [30], and conformable fractional gradient-based system [31].
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