• Journal of the military operations research society of Korea
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• v.25 no.2
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• pp.97-105
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• 1999

When infeasible interior-point methods are applied to large-scale linear programming problems, they become unstable and cannot solve the problems if convergence rates of primal feasibility, dual feasibility and duality gap are not well-balanced. We can balance convergence rates of primal feasibility, dual feasibility and duality gap by introducing control parameters. As a result, the stability and the efficiency of infeasible interior-point methods can be improved.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.24-29
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• 1996

If the LP problem doesn't have the optimal soultion uniquely, the solution fo the primal-dual barrier method converges to the interior point of the optimal face. Therefore, when the optimal vertex solution or the optimal basis is required, we have to perform the additional procedure to recover the optimal basis from the final solution of the interior point method. In this paper the exisiting methods for recovering the optimal basis or identifying the optimal solutions are analyzed and the new methods are suggested. This paper treats the two optimal basis recovery methods. One uses the purification scheme and the simplex method, the other uses the optimal face solutions. In the method using the purification procedure and the simplex method, the basic feasible solution is obtained from the given interior solution and then simplex method is performed for recovering the optimal basis. In the method using the optimal face solutions, the optimal basis in the primal-dual barrier method is constructed by intergrating the optimal solution identification technique and the optimal basis extracting method from the primal-optimal soltion and the dual-optimal solution.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.6
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• pp.2095-2110
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• 2015

This paper presents a design for a throughput-efficient online relay selection scheme for dual-hop multi-relay cooperative networks. Problems arise with these networks due to unpredictability of the relaying link quality and high time-consumption to probe the dual-hop link. In this paper, we firstly propose a novel probing and relaying protocol, which greatly reduces the overhead of the dual-hop link estimation by leveraging the wireless broadcasting nature of the network. We then formulate an opportunistic relay selection process for the online decision-making, which uses a tradeoff between obtaining more link information to establish better cooperative relaying and minimizing the time cost for dual-hop link estimation to achieve higher throughput. Dynamic programming is used to construct the throughput-optimal control policy for a typically heterogeneous Rayleigh fading environment, and determines which relay to probe and when to transmit the data. Additionally, we extend the main results to mixed Rayleigh/Rician link scenarios, i.e., where one side of the relaying link experiences Rayleigh fading while the other has Rician distribution. Numerical results validate the effectiveness and superiority of our proposed relaying scheme, e.g., it achieves at least 107% throughput gain compared with the state of the art solution.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.491-505
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• 1997

This paper deals with the formulation and solution of a wide class of structures, in the presence of both geometric and material nonlinearities, as a particular mathematical programming problem. We first present key ideas for the nonholonomic (path dependent) rate formulation for a suitably discretized structural model before we develop its computationally advantageous stepwise holonomic (path independent) counterpart. A feature of the final mathematical programming problem, known as a nonlinear complementarity problem, is that the governing relations exhibit symmetry as a result of the introduction of so-called nonlinear "residuals". One advantage of this form is that it facilitates application of a particular iterative algorithm, in essence a predictor-corrector method, for the solution process. As an illustrative example, we specifically consider the simplest case of plane trusses and detail in particular the general methodology for establishing the static-kinematic relations in a dual format. Extension to other skeletal structures is conceptually transparent. Some numerical examples are presented to illustrate applicability of the procedure.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.85-97
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• 2003

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

• 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.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.759-772
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• 2012

In this paper, semi-infinite constrained programming, a class of constrained nonsmooth optimization problems, are transformed into unconstrained nonsmooth convex programs under the help of exact penalty function. The unconstrained objective function which owns the primal-dual gradient structure has connection with $\mathcal{VU}$-space decomposition. Then a $\mathcal{VU}$-space decomposition method can be applied for solving this unconstrained programs. Finally, the superlinear convergence algorithm is proved under certain assumption.

• 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.

• Korean Management Science Review
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• v.11 no.3
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• pp.35-46
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• 1994

The primal-dual log barrier code OB1(Optimization with Barriers 1) has been identified the most efficient one in reducing computer time and solving large linear programs. This is a brief survey of OB1's life-time and performance.