• Journal of Korea Multimedia Society
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• v.9 no.12
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• pp.1636-1648
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• 2006

In this paper, we propose a new optimization approach to the rate control problem in a wired-cum-wireless network. A primal-dual interior-point(PDIP) algorithm is used to find the solution of the rate optimization problem. We show a comparison between the dual-based(DB) algorithm and PDIP algorithm for solving the rate control problem in the wired-cum-wireless network. The PDIP algorithm performs much better than the DB algorithm. The PDIP can be considered as an attractive method to solve the rate control problem in network. We also present a numerical example and simulation to illustrate our conclusions.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.139-152
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• 2003

In this paper, we characterize a vector-valued convex set function by its epigraph. The concepts of a vector-valued set function and a vector-valued concave set function we given respectively. The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced. Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.1
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• pp.321-344
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• 2017

Smart homes are the new generation of homes where pervasive computing is employed to make the lives of the residents more convenient. Human activity recognition (HAR) is a fundamental task in these environments. Since critical decisions will be made based on HAR results, accurate recognition of human activities with low uncertainty is of crucial importance. In this paper, a novel HAR method based on a difference of convex programming (DCP) problem is represented, which manages to handle uncertainty. For this purpose, given an input sensor data stream, a primary belief in each activity is calculated for the sensor events. Since the primary beliefs are calculated based on some abstractions, they naturally bear an amount of uncertainty. To mitigate the effect of the uncertainty, a DCP problem is defined and solved to yield secondary beliefs. In this procedure, the uncertainty stemming from a sensor event is alleviated by its neighboring sensor events in the input stream. The final activity inference is based on the secondary beliefs. The proposed method is evaluated using a well-known and publicly available dataset. It is compared to four HAR schemes, which are based on temporal probabilistic graphical models, and a convex optimization-based HAR procedure, as benchmarks. The proposed method outperforms the benchmarks, having an acceptable accuracy of 82.61%, and an average F-measure of 82.3%.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.11
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• pp.771-781
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• 2022

Sequential convex programming based performance analysis of the designed UAV is performed. The nonlinear optimization problems generated by aerodynamics are approximated to socond order program by discretization and convexification. To improve the performance of the algorithm, the solution of the relaxed problem is used as the initial trajectory. Dive trajectory optimization problem is analyzed through iterative solution procedure of approximated problem. Finally, the maximum final velocity according to the performance of the actuator model was compared.

• Journal of the Korean Statistical Society
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• v.1 no.1
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• pp.18-24
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• 1973

Study on convexity has been improved in many statistical fields, such as linear programming, stochastic inverntory problems and decision theory. In proof of main theorem in Section 3, M. Loeve already proved this theorem with the $r$-th absolute moments on page 160 in [1]. Main consideration is given to prove this theorem using convex theorems with the generalized $t$-th mean when some convex properties hold on a real linear vector space $R_N$, which satisfies all properties of finite dimensional Hilbert space. Throughout this paper $\b{x}_j, \b{y}_j$ where $j = 1,2,......,k,.....,N$, denotes the vectors on $R_N$, and $C_N$ also denotes a subspace of $R_N$.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.2
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• pp.117-127
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• 2000

In this paper, we propose a new convex combination weight rule for the cross decomposition method which is known to be one of the most reliable and promising strategies for the large scale optimization problems. It is called generalized cross decomposition, a modification of linear mean value cross decomposition for specially structured linear programming problems. This scheme puts more weights on the recent subproblem solutions other than the average. With this strategy, we are having more room for selecting convex combination weights depending on the problem structure and the convergence behavior, and then, we may choose a rule for either faster convergence for getting quick bounds or more accurate solution. Also, we can improve the slow end-tail behavior by using some combined rules. Also, we provide some computational test results that show the superiority of this strategy to the mean value cross decomposition in computational time and the quality of bounds.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.111-125
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• 2012

In this paper, we introduce new classes of generalized convex n-set functions called $d$-weak strictly pseudo-quasi type-I univex, $d$-strong pseudo-quasi type-I univex and $d$-weak strictly pseudo type-I univex functions and focus our study on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions of aforesaid functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the involved functions satisfy appropriate generalized $d$-type-I univexity conditions.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.10a
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• pp.419-424
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• 1999

In this paper, the comparison of the first order approximation schemes such as SLP (sequential linear programming), CONLIN(convex linearization), MMA(method of moving asymptotes) and the second order approximation scheme, SQP(sequential quadratic programming) was accomplished for optimization of and nonlinear structures. It was found that MMA and SQP(sequential quadratic programming) was accomplished for optimization of and nonlinear structures. It was found that MMA and SQP are the most efficient methods for optimization. But the number of function call of SQP is much more than that of MMA. Therefore, when it is considered with the expense of computation, MMA is more efficient than SQP. In order to examine the efficiency of MMA for complex optimization problem, it was applied to the helicopter tail boom considering column buckling and local wall buckling constraints. It is concluded that MMA can be a very efficient approximation scheme from simple problems to complex problems.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.727-753
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• 2013

In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivex functions, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-pseudosounivex functions, and ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.