Coefficients of Modified Broyden Method and Its Global Convergence

Ibrahim, Mohd Asrul Hery; Zakaria, Zahratul Amani; Mamat, Mustafa; Sofi, Azfi Zaidi Mohammad

doi:10.17654/ms100050795

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A New Proposed Search Direction2

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2019

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(3 citation statements)

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“…In this section, we advise a replacement search direction as deduced from Ibrahim et al [9][10][11]. The new search direction is outlined as…”

Section: A New Proposed Search Directionmentioning

confidence: 99%

“…So to prove our new theorem, we have a tendency to necessarily use the subsequent given assumptions (see Section 2.1). [9,11,13] (A1) f : R n → R is twice continuously differentiable.…”

Section: A New Proposed Search Directionmentioning

confidence: 99%

“…Matrix I is the identity and <0. In addition, Ibrahim et al [11] propose another search direction that is outlined as…”

Section: Introductionmentioning

confidence: 99%

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A New Hybrid Algorithm for Convex Nonlinear Unconstrained Optimization

Hamed

Ahmed

Al-Bayati³

2019

Journal of Applied Mathematics

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In this study, we tend to propose a replacement hybrid algorithmic rule which mixes the search directions like Steepest Descent (SD) and Quasi-Newton (QN). First, we tend to develop a replacement search direction for combined conjugate gradient (CG) and QN strategies. Second, we tend to depict a replacement positive CG methodology that possesses the adequate descent property with sturdy Wolfe line search. We tend to conjointly prove a replacement theorem to make sure global convergence property is underneath some given conditions. Our numerical results show that the new algorithmic rule is powerful as compared to different standard high scale CG strategies.

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“…In this section, we advise a replacement search direction as deduced from Ibrahim et al [9][10][11]. The new search direction is outlined as…”

Section: A New Proposed Search Directionmentioning

confidence: 99%

“…So to prove our new theorem, we have a tendency to necessarily use the subsequent given assumptions (see Section 2.1). [9,11,13] (A1) f : R n → R is twice continuously differentiable.…”

Section: A New Proposed Search Directionmentioning

confidence: 99%