Convergence analysis of a new conjugate gradient method for unconstrained optimization

Abdullahi, Ibrahim; Ahmad, Rais

doi:10.12988/ams.2015.510686

Cited by 3 publications

(6 citation statements)

References 19 publications

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“…This section introduces weighted analytic center for the system of second order cone constraints (1).…”

Section: Weighted Analytic Center For Second Order Cone Constraintsmentioning

confidence: 99%

“…Table 2 describes the 31 random test problems used for our numerical experiments. For each SOC test problem, integer values q and n are generated uniformly in the intervals [1,6] and [2,10] respectively. Then q m ∈ ℤ is generated such that each entry i m is uniform in the interval [1,10].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…For each SOC test problem, integer values q and n are generated uniformly in the intervals [1,6] and [2,10] respectively. Then q m ∈ ℤ is generated such that each entry i m is uniform in the interval [1,10]. After this, q SOCs of the form 0…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…denotes the feasible region defined by the SOC constraints in (1). Assume R is bounded and that it has a non-empty interior.…”

Section: Introductionmentioning

confidence: 99%

“…CG methods are popular for solving large scale non-linear unconstrained optimization problems. They are characterized by strong global convergence properties and low memory requirement [1]. CG methods use only the gradient of the barrier function.…”

Section: Introductionmentioning

confidence: 99%

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A Weighted Analytic Center for Second-Order Cone Constraints

Dawuda¹,

Jibrin²,

Abdullahi³

2021

ACM

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This paper introduces a weighted analytic center for a system of second order cone constraints. The associated barrier function is shown to be convex and conjugate gradient (CG) methods are used to compute the weighted analytic center. In contrast with Newton's-like methods, CG methods use only the gradient and not the Hessian to minimize a function. The methods considered are the HPRP and ZA with exact and inexact line searches. The exact line search uses Newton's method and quadratic interpolation is used for the inexact line search. The performance of each method on random test problems was evaluated by observing the number of iterations and time required to find the weighted analytic center. Our numerical methods indicate that ZA is better than HPRP with any of the two line searches, in terms of the number of iterations and time to find the weighted analytic center. Quadratic interpolation inexact line search gives the best success rate and fewest number of iterations for the CG methods considered. On the other hand, the fastest time for the CG methods is found with the Newton's exact line search. In addition, these results indicate that for each of the methods, our Quadratic interpolation inexact line search has a higher cost per iteration than that of the Newton's exact line search.

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“…This section introduces weighted analytic center for the system of second order cone constraints (1).…”

Section: Weighted Analytic Center For Second Order Cone Constraintsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

“…denotes the feasible region defined by the SOC constraints in (1). Assume R is bounded and that it has a non-empty interior.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Weighted Analytic Center for Second-Order Cone Constraints

Dawuda¹,

Jibrin²,

Abdullahi³

2021

ACM

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Conjugate Gradient Methods for Computing Weighted Analytic Center for Linear Matrix Inequalities Using Exact and Quadratic Interpolation Line Searches

Jibrin¹,

Abdullahi²

2020

AJAM

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Global Convergence Analysis of a Modified Conjugate Gradient Method for Unconstrained Optimization Problems

Alilu,

Ibrahim,

Usman

2024

FJS

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In this paper, the global convergence analysis of a modified conjugate gradient method for solving unconstrained optimization problems was considered. We proposed a modified conjugate gradient method for solving unconstrained optimization problems that incorporates an adaptive step size selection scheme. We analyze the method’s global convergence properties theoretically, demonstrating that it satisfies the sufficient descent and global convergence conditions under various assumptions. And we provide numerical experiments to illustrate its effectiveness and efficiency in solving unconstrained optimization problems. We also compare the numerical performance of the proposed method against three existing methods namely, FR, HS and PR using MATLAB simulations. The proposed method was found to perform better than FR and HS, and in competition with PR with respect to computation time, number of iteration and function evaluation.

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Convergence analysis of a new conjugate gradient method for unconstrained optimization

Cited by 3 publications

References 19 publications

A Weighted Analytic Center for Second-Order Cone Constraints

A Weighted Analytic Center for Second-Order Cone Constraints

Conjugate Gradient Methods for Computing Weighted Analytic Center for Linear Matrix Inequalities Using Exact and Quadratic Interpolation Line Searches

Global Convergence Analysis of a Modified Conjugate Gradient Method for Unconstrained Optimization Problems

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