• Kyungpook Mathematical Journal
• /
• v.47 no.2
• /
• pp.239-251
• /
• 2007

We show how the minimization can be used to solve the quadratic matrix equation and then compare two different types of conjugate gradient method which are Polak and Ribi$\acute{e}$re version and Fletcher and Reeves version. Finally, some results of the global and local convergence are shown.

• 제어로봇시스템학회:학술대회논문집
• /
• 1996.10b
• /
• pp.466-469
• /
• 1996

In this paper, we present the global minimization condition by an informal analysis of the Langevine competitive learning neural network. From the viewpoint of the stochastic process, it is important that competitive learning guarantees an optimal solution for pattern recognition. By analysis of the Fokker-Plank equation for the proposed neural network, we show that if an energy function has a special pseudo-convexity, Langevine competitive learning can find the global minima. Experimental results for pattern recognition of handwritten numeral data indicate the superiority of the proposed algorithm.

• 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 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 the Korea Society of Computer and Information
• /
• v.20 no.7
• /
• pp.41-47
• /
• 2015

The bandwidth minimization problem (BMP) has been classified as NP-complete because the polynomial time algorithm to find the optimal solution has been unknown yet. This paper suggests polynomial time heuristic algorithm is to find the solution of bandwidth minimization problem. To find the minimum bandwidth ${\phi}^*=_{min}{\phi}(G)$, ${\phi}(G)=_{max}\{{\mid}f(v_i)-f(v_j):v_i,v_j{\in}E\}$ for given graph G=(V,E), m=|V|,n=|E|, the proposed algorithm sets the maximum degree vertex $v_i$ in graph G into global central point (GCP), and labels the median value ${\lceil}m+1/2{\rceil}$ between [1,m] range. The graph G is partitioned into subgroup, the maximum degree vertex in each subgroup is set to local central point (LCP), and we adjust the label of LCP per each subgroup as possible as minimum distance from GCP. The proposed algorithm requires O(mn) time complexity for label to all of vertices. For various twelve graph, the proposed algorithm can be obtains the same result as known optimal solution. For one graph, the proposed algorithm can be improve on known solution.

• IE interfaces
• /
• v.8 no.1
• /
• pp.23-30
• /
• 1995

Optimization in the engineering design is to select the best of many possible design alternatives in a complex design space. One major problem of local minimization algorithm is that they often result in local optima. In this paper, a hybrid method was developed by coupling the genetic algorithm and a traditional direct search method. The proposed method first finds a region for possible global optimum using the genetic algorithm and then searchs for a global optimum using the direct search method. To evaluate the performance of the hybrid method, it was applied to three test problems and a problem of designing corrugate bulkhead of a ship.

• 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.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.2
• /
• pp.406-414
• /
• 2002

A new approach, referred to as a successive zooming genetic algorithm (SZGA), is Proposed for identifying a global solution for continuous optimization problems. In order to improve the local fine-tuning capability of GA, we introduced a new method whereby the search space is zoomed around the design point with the best fitness per 100 generation. Furthermore, the reliability of the optimized solution is determined based on the theory of probability. To demonstrate the superiority of the proposed algorithm, a simple genetic algorithm, micro genetic algorithm, and the proposed algorithm were tested as regards for the minimization of a multiminima function as well as simple functions. The results confirmed that the proposed SZGA significantly improved the ability of the algorithm to identify a precise global minimum. As an example of structural optimization, the SZGA was applied to the optimal location of support points for weight minimization in the radial gate of a dam structure. The proposed algorithm identified a more exact optimum value than the standard genetic algorithms.

• Transactions of Materials Processing
• /
• v.9 no.4
• /
• pp.404-412
• /
• 2000

It is desirable to use the square grid analysis with the aid of the stereo vision and image processing techniques in order to automatically measure the surface-strain distribution over a stamped part. But this method has some inherent problems such as the difficulty in enhancement of bad images, the measurement error due to the digital image resolution and the limit of the area that can be measured at a time. Therefore, it is still hard to measure the strain distribution over the entire surface of a medium-or large-sized stamped part even by using an automated strain measurement system. In this study, several methods which enable to solve these problems considerably without losing accuracy and precision In measurement are suggested. The superposition of images that have different high-lightened or damaged part from each other gives much enhanced image. A new algorithm for constructing of the element connectivity from the line-thinned image helps recognize up to 1,000 elements. And the geometry assembling algorithm including the global error minimization makes it possible to measure a large specimen with reliability and efficiency.