Symmetric Rank-One Method for Solving Large-Scale Optimization Problems

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Modarres Khiabani F.; DANESHIAN B.

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Journal: Journal of Operational Research in its Applications Year:2019 | Volume:15 | Issue:4 (59) Page(s): 151-170

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Information Journal Paper

Title

Symmetric Rank-One Method for Solving Large-Scale Optimization Problems

Author(s)

Modarres Khiabani F. | DANESHIAN B. | Issue Writer Certificate

Keywords

Unconstrained OptimizationQ2

Ordinary Differential EquationsQ2

Limited Memory MethodsQ1

Line-SearchQ1

Trust-RegionQ1

Abstract

The search for finding the local minimization in Unconstrained Optimization problems and a fixed point of the gradient system of Ordinary Differential Equations are two close problems. Limited-memory algorithms are widely used to solve large-scale problems, while Rang Kuta's methods are also used to solve numerical differential equations. In this paper, using the concept of sub-space method and fixed-step length and integration of Line-Search and Trust-Region techniques, an ODE-based hybrid method is proposed for solving large-scale optimization problems. Since the Line-Search methods may require more iteration for convergence, while Trust-Region methods also require a lot of iteration to solve the constrained sub problem, a new class of methods is proposed in this way, which combines the best features of Trust-Region and Line-Search methods. The main feature of the proposed method is that the linear equation system is solved only once in order to obtain the experimental step.

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APA: Copy

Modarres Khiabani, F., & DANESHIAN, B.. (2019). Symmetric Rank-One Method for Solving Large-Scale Optimization Problems. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), 15(4 (59) ), 151-170. SID. https://sid.ir/paper/164489/en

Vancouver: Copy

Modarres Khiabani F., DANESHIAN B.. Symmetric Rank-One Method for Solving Large-Scale Optimization Problems. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS)[Internet]. 2019;15(4 (59) ):151-170. Available from: https://sid.ir/paper/164489/en

IEEE: Copy

F. Modarres Khiabani, and B. DANESHIAN, “Symmetric Rank-One Method for Solving Large-Scale Optimization Problems,” JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), vol. 15, no. 4 (59) , pp. 151–170, 2019, [Online]. Available: https://sid.ir/paper/164489/en

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