• 대한수학회논문집
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• 제33권2호
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• pp.671-676
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• 2018

In this paper we prove that the gradient ideal of a Morse polynomial is radical. This gives a generic class of polynomials whose gradient ideals are radical. As a consequence we reclaim a previous result that the unconstrained polynomial optimization problem for Morse polynomials has a finite convergence.

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.701-716
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• 1998

In this paper we develop algorithms in programming lan-guage SCHEME for implementation of the main first order gradient techniques for unconstrained optimization. Implementation of the de-scent techniques which use non-optimal descent steps as well as imple-mentation of the optimal descent techniques are described. Also we investigate implementation of the global problem called optimization along a line. Developed programs are effective and simpler with re-spect to the corresponding in the procedural programming languages. Several numerical examples are reported.

• 한국통신학회논문지
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• 제29권10C호
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• pp.1402-1413
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• 2004

비강체 (non-rigid) 영상 등록에서 추정되는 좌표변환은 가역이어야 함으로 그 변환의 Jacobian 행렬식은 항상 양수 값을 가져야 한다. 본 논문에서는 이러한 가역 조건을 만족하는 좌표변환의 조건을 gradient 크기 제한의 조건으로 구한다. 또한 cubic B-spline을 이용한 변환 모델의 경우, 이 gradient 크기 제한 조건을 만족시키는 인수 집합을 이웃한 두 계수들의 차이가 제한된 인수들의 집합으로 구하였다. 이러한 인수들의 집합은 half space들의 교집합으로 이루어진 convex 집합이다. 본 논문에서는 이 convex 집합에 속하는 인수로 구성되는 좌표변환들 중에서 유사지수 (similarity measure) 를 최대로 만드는 변환을 gradient projection 최적화 기법을 통해 발견하였다. 이론적 분석, 폐 CT (Computed Tomography) 영상을 이용한 시뮬레이션 및 실험을 통하여, 제안된 알고리즘의 성능이 벌칙 함수 penalty function) 를 이용하는 기존의 방법보다 우수함을 증명하였다.

• 산업경영시스템학회지
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• 제15권26호
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• pp.67-76
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• 1992

변수의 어떤 값들에 대해 도함수를 가질 수 없는 함수를 최적화해야 하는 등. OR 에서는 여러 상황이 존재한다. 이것은 Convex Analysis〔12〕서 이론적인 differential calculus를 근저로 하는 Non-differentiable Optimization 또는 Non-smooth Optimization 을 취급하는 것이 된다. 이러한 종류의 미분이 가능하지 않은 최적화문제는 연속함수를 위한 종래의 최적화법으로는 그 해법자체가 갖고 있는 연속성의 한계를 극복할 수 없다. 따라서, 이러한 문제를 해결하기 위해 Demyanov〔4〕가 제시한 quasi-differental function의 정의와 이들 함수에 따른 몇가지 주요정리들을 언급하고, 그것들을 토대로 Non-differentiable optimization problem의 수치적인 방법을 수행하기 위해 일종의 modified gradient 법을 제시한다. 이를 이용해서 numerical experiment를 위한 방법을 구체화하여, unrestricted non-differentable optimization problem에 적응하여, 그 수치해 결과를 보여서 그 타당성음 검토하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권3호
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• pp.107-116
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• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.

• 대한기계학회논문집A
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• 제32권12호
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• pp.1132-1139
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• 2008

The aim of this study is to apply shape optimization technique for the repair of aging airframe components, which may extend fatigue life substantially. Free-form optimum shapes of a cracked part to be reworked or replaced are investigated with the objective to minimize the peak local stress concentration or fatigue-damage. Iterative non-gradient method, which is based on an analogy with biological growth, is employed by incorporating the robust optimization method to take account of the stochastic nature of the loading conditions. Numerical examples of optimal hole shape in a flat plate are presented to validate the proposed method. The method is then applied to determine the reworked or replacement shape for the repair of a cracked rib in the rear assembly wing body of aircraft.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.461-466
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• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.335-342
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• 2002

A continuum-based design sensitivity analysis (DSA) method fur non-shape problems is developed for geometrically nonlinear elastic structures. The non-shape problem is characterized by the design variables that are not associated with the domain of system like sizing, material property, loading, and so on. Total Lagrangian formulation with the Green-Lagrange strain and the second Piola-Kirchhoff stress is employed to describe the geometrically nonlinear structures. The spatial domain is discretized using the 4-node isoparametric plane stress/strain elements. The resulting nonlinear system is solved using the Newton-Raphson iterative method. To take advantage of the derived analytical sensitivity In topology optimization, a fast and efficient design sensitivity analysis method, adjoint variable method, is employed and the material property of each element is selected as non-shape design variable. Combining the design sensitivity analysis method and a gradient-based design optimization algorithm, an automated design optimization method is developed. The comparison of the analytical sensitivity with the finite difference results shows excellent agreement. Also application to the topology design optimization problem suggests a very good insight for the layout design.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권1호
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• pp.319-333
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• 2022

In order to enhance system energy efficiency, bidirectional link resource allocation strategy in GFDM-based multiuser SWIPT systems is proposed. In the downlink channel, each SWIPT user applies power splitting (PS) receiver structure in information decoding (ID) and non-linear energy harvesting (EH). In the uplink channel, information transmission power is originated from the harvested energy. An optimization problem is constructed to maximize weighted sum ID achievable rates in the downlink and uplink channels via bidirectional link power allocation as well as subcarriers and subsymbols scheduling. To solve this non-convex optimization problem, Lagrange duality method, sub-gradient-based method and greedy algorithm are adopted respectively. Simulation results show that the proposed strategy is superior to the fixed subcarrier scheme regardless of the weighting coefficients. It is superior to the heuristic algorithm in larger weighting coefficients scenario.

• 제어로봇시스템학회논문지
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• 제21권3호
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• pp.233-236
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• 2015

In this paper, a nonlinear optimization problem is proposed to obtain a structured static output feedback controller for discrete time linear systems. The proposed optimization problem has LMI (Linear Matrix Inequality) constraints and a non-convex objective function. Using the conditional gradient method, we can obtain suboptimal solutions of the proposed optimization problem. Numerical examples show the effectives of the proposed approach.