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1

A new optimization method based on Perry's idea through the use of the matrix power

Hafaidia Imane, Benrabia Noureddine, Ghiat Mourad, Guebbai Hamza

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 4

29--41

EN

The purpose of this paper is to present a new conjugate gradient method for solving unconstrained nonlinear optimization problems, based on Perry’s idea. An accelerated adaptive algorithm is proposed, where our search direction satisfies the sufficient descent condition. The global convergence is analyzed using the spectral analysis. The numerical results are described for a set of standard test problems, and it is shown that the performance of the proposed method is better than that of the CG-DESCENT, the mBFGS and the SPDOC.

2

Two New Decomposition Algorithms for Training Bound-Constrained Support Vector Machines

Niu L., Zhou R., Zhao X., Shi Y.

Foundations of Computing and Decision Sciences

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2015

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Vol. 40, No. 1

67--86

EN

Bound-constrained Support Vector Machine(SVM) is one of the stateof- art model for binary classification. The decomposition method is currently one of the major methods for training SVMs, especially when the nonlinear kernel is used. In this paper, we proposed two new decomposition algorithms for training bound-constrained SVMs. Projected gradient algorithm and interior point method are combined together to solve the quadratic subproblem effciently. The main difference between the two algorithms is the way of choosing working set. The first one only uses first order derivative information of the model for simplicity. The second one incorporate part of second order information into the process of working set selection, besides the gradient. Both algorithms are proved to be global convergent in theory. New algorithms is compared with the famous package BSVM. Numerical experiments on several public data sets validate the effciency of the proposed methods.

3

A New Non-monotone Line Search Algorithm for Nonlinear Programming

Zhang J.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 7b

265--268

EN

We study the application of a kind of non-monotone line search’s technique in conjugate gradient method. At present, most of the study of conjugate gradient methods are using Wolfe’s monotone line search, by constructing the condition of Zoutendijk, we can get the conclusion that it’s convergence by using reduction to absurdity. Here we study the global convergence of conjugate gradient methods with Armijo-type line search, the thought of proof wasn’t using the method above mentioned.

PL

Przeprowadzono studia nad zastosowaniem niemonotonicznego badania prostej w sprzężonej metodzie gradientowej. Obecnie najczęściej wykorzystuje się metodę Wolfa ale nasze badania wykazały że lepsze wyniki uzyskuje się w metodach globalnej zbieżności sprzężonej metody gradientowej.

4

A Convergence Proof for the Particle Swarm Optimiser

Bergh F. van den, Engelbrecht A.P.

Fundamenta Informaticae

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2011

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Vol. 105, nr 4

341-374

EN

The Particle Swarm Optimiser (PSO) is a population based stochastic optimisation algorithm, empirically shown to be efficient and robust. This paper provides a proof to show that the original PSO does not have guaranteed convergence to a local optimum. A flaw in the original PSO is identified which causes stagnation of the swarm. Correction of this flaw results in a PSO algorithm with guaranteed convergence to a local minimum. Further extensions with provable global convergence are also described. Experimental results are provided to elucidate the behavior of the modified PSO as well as PSO variations with global convergence.