• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.567-579
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• 2009

Recently, Peng et al. proposed a primal-dual interior-point method with new search direction and self-regular proximity for LP. This new large-update method has the currently best theoretical performance with polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$). In this paper we use this search direction to propose a primal-dual interior-point method for convex quadratic programming (QP). We overcome the difficulty in analyzing the complexity of the primal-dual interior-point methods for convex quadratic programming, and obtain the same polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$) for convex quadratic programming.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.371-384
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• 2005

Usual symmetric duality results are proved for Wolfe and Mond-Weir type nondifferentiable nonlinear symmetric dual programs under F-convexity F-concavity and F-pseudoconvexity F-pseudoconcavity assumptions. These duality results are then used to formulate Wolfe and Mond-Weir type nondifferentiable minimax mixed integer dual programs and symmetric duality theorems are established. Moreover, nondifferentiable fractional symmetric dual programs are studied by using the above programs.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.719-738
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• 2000

A dual algorithm based on the smooth function proposed by Polyak (1988) is constructed for solving nonlinear programming problems with inequality constraints. It generates a sequence of points converging locally to a Kuhn-Tucker point by solving an unconstrained minimizer of a smooth potential function with a parameter. We study the relationship between eigenvalues of the Hessian of this smooth potential function and the parameter, which is useful for analyzing the effectiveness of the dual algorithm.

• Journal of the Korean Operations Research and Management Science Society
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• v.24 no.1
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• pp.27-38
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• 1999

In this paper, Primal-Interior Dual-Simplex method(PIDS) and Dual-Interior Primal-Simplex method(DIPS) are developed for the general bounded linear programming. Two methods were implemented and compared with other pricing techniques for the Netlib. linear programming problems. For the PIDS, it shows superior performance to both most nagative rule and dual steepest-edge method since it practically reduces degenerate iterations and has property to reduce the problem. For the DIPS, pt requires less iterations and computational time than least reduced cost method. but it shows inferior performance to the dynamic primal steepest-edge method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.1C
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• pp.90-97
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• 2009

The advantages of the orthogonal frequency division multiplexing (OFDM) are high spectral efficiency, resiliency to RF interference, and lower multi-path distortion. To further utilize vast channel capacity of the multiuser OFDM, one has to find the efficient adaptive subchannel and bit allocation among users. In this paper, we propose an 0-1 integer programming model formulating the optimal subchannel and bit allocation problem of the multiuser OFDM. We employ a dual-decomposition method that provides a tight linear programming (LP) relaxation bound. Simulation results are provided to show the effectiveness of the 0-1 integer programming model. MATLAB simulation on a system employing M-ary quardarature amplitude modulation (MQAM) assuming a frequency-selective channel consisting of three independent Rayleigh multi-paths are carried with the optimal subchannel and bit allocation solution generated by 0-1 integer programming model.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.603-619
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• 2009

Wolfe and Mond-Weir type dual to a nondifferentiable continuous programming containing support functions are formulated and duality is investigated for these two dual models under invexity and generalized invexity. A close relationship of our duality results with those of nondifferentiable nonlinear programming problem is also pointed out.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.2
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• pp.147-156
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• 1993

Recently a new concept of shadow prices, called average shadow price, has been developed. This paper provides a dual problem and the corresponding duality theorems justifying this new shadow price. The general duality framework is used. As an important secondary result, a new reduced class of price function, the pp. h.-class, has been developed for the general duality theory. This should be distinguished from other known reductions achieved in some specific areas of mathematical programming, in that it sustains the strong duality property in all the mathematical programs. The new general dual problem suggested with this pp. h.-class provides, as an optimal solution, the average shadow prices.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.75-106
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• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.411-423
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• 2012

A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are ${\eta}$-semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-in nite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.

• Korean Management Science Review
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• v.11 no.3
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• pp.1-11
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• 1994

Recent advances in linear programming solution methodology have focused on interior point methods. This powerful new class of methods achieves significant reductions in computer time for large linear programs and solves problems significantly larger than previously possible. These methods can be examined from points of Fiacco and McCormick's barrier method, Lagrangian duality, Newton's method, and others. This study presents a primal-dual log barrier algorithm of interior point methods for linear programming. The primal-dual log barrier method is currently the most efficient and successful variant of interior point methods. This paper also addresses a Cholesky factorization method of symmetric positive definite matrices arising in interior point methods. A special structure of the matrices, called supernode, is exploited to use computational techniques such as direct addressing and loop-unrolling. Two dense matrix handling techniques are also presented to handle dense columns of the original matrix A. The two techniques may minimize storage requirement for factor matrix L and a smaller number of arithmetic operations in the matrix L computation.