• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.461-466
• /
• 2006

In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.8 no.2
• /
• pp.7-13
• /
• 2004

A Conjugate Gradient (CG) algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and is designed for the minimization of general nonlinear functions. It compares favorably in numerical tests with the original Dixon algorithm on which the new algorithm is based.

• Journal of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1253-1267
• /
• 2010

This paper considers the unconstrained global optimization with the revised filled function methods. The minimization sequence could leave from a local minimizer to a better minimizer of the objective function through minimizing an auxiliary function constructed at the local minimizer. Some promising numerical results are also included.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.367-376
• /
• 2007

In this paper we consider the global convergence of a new super memory gradient method for unconstrained optimization problems. New trust region radius is proposed to make the new method converge stably and averagely, and it will be suitable to solve large scale minimization problems. Some global convergence results are obtained under some mild conditions. Numerical results show that this new method is effective and stable in practical computation.

• Proceedings of the KIEE Conference
• /
• 2000.07b
• /
• pp.744-746
• /
• 2000

This paper presents an optimum design of a linear induction motor(LIM) using genetic algorithm(GA). Sequential unconstrained minimization technique(SUMT) is used to transform the nonlinear optimization with constraints to a simple unconstrained problem. The objective functions of LIM such as trust, weight are optimized and the result was applied to the design of linear induction pump.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.311-319
• /
• 2007

This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation $B_k+1{^s}_k=yk\;where\;y_k^*=yk+A_ks_k\;and\;A_k$ is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.

• Journal of Korean Society of Steel Construction
• /
• v.16 no.1 s.68
• /
• pp.21-32
• /
• 2004

In this study, a continuous optimum design model with its application program for plane steel frame structures developed. In the model, the sequential unconstrained minimization technique (SUMT) transforming the nonlinear optimization problem with multidesign variables and constraints into an unconstrained minimization problem and the refined plastic hinge analysis method as one of the most effective second-order inelastic analysis methods for steel frame structures were implemented. The total weight of a steel frame structure was taken as the objective function, and the AISC-LRFD code requirements for the local and member buckling, flexural strength, shear strength, axial strength and size of the cross-sectional shapes of members were used for the derivation of constraint equations. To verify the appropriateness of the present model, the optimum designs of serveral plane steel frame structures subject to vertical and horizontal loads were conducted.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.1
• /
• pp.55-61
• /
• 2005

A Conjugate Gradient algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and for general functions. It compares favourably in numerical tests (over eight test functions and dimensionality up to 1000) with the Dixon (1975) algorithm on which this new algorithm is based.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.325-331
• /
• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• Journal of the korean Society of Automotive Engineers
• /
• v.4 no.2
• /
• pp.79-85
• /
• 1982

Computer codes on two numerical optimization methods-Sequentially Unconstrained Minimization Technique (SUMT) and Gradient Projection Method-are constructed and tested with several test problems. Design formulation of tension - compression coil spring is set up and the solution is obtained. Consequently, the feature, the advantage and the limitation of these methods, made clear through the tests, are discussed.