• Journal of applied mathematics & informatics
• /
• v.5 no.3
• /
• pp.797-804
• /
• 1998

A pair of multiobjective generalized symmetric dual non-linear programming problems and weak strong and converse dual-ity theorems for these problems are established under generalized $\rho-(\eta,0)$-invexity assumptions. Several known results are obtained as special cases.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1395-1408
• /
• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.14 no.2
• /
• pp.19-26
• /
• 1989

We in this paper have defined the concept of .epsilon.-symmetric relation between the Lagrangean relaxation and the Benders' decomposition. This links the solutions of the Lagrangean subproblems and those of the Benders' subproblems even under positive duality gaps. As an application we have discussed the reduction of the size for a special class of problems.

• Journal of KIISE:Databases
• /
• v.33 no.3
• /
• pp.310-326
• /
• 2006

In this paper, we deal with a method of efficiently processing continuous queries in a data stream environment. We classify previous query processing methods into two dual categories - data-initiative and query-initiative - depending on whether query processing is initiated by selecting a data element or a query. This classification stems from the fact that data and queries have been treated asymmetrically. For processing continuous queries, only data-initiative methods have traditionally been employed, and thus, the performance gain that could be obtained by query-initiative methods has been overlooked. To solve this problem, we focus on an observation that data and queries can be treated symmetrically. In this paper, we propose the duality model of data and queries and, based on this model, present a new viewpoint of transforming the continuous query processing problem to a multi-dimensional spatial join problem. We also present a continuous query processing algorithm based on spatial join, named Spatial Join CQ. Spatial Join CQ processes continuous queries by finding the pairs of overlapping regions from a set of data elements and a set of queries defined as regions in the multi-dimensional space. The algorithm achieves the effects of both of the two dual methods by using the spatial join, which is a symmetric operation. Experimental results show that the proposed algorithm outperforms earlier methods by up to 36 times for simple selection continuous queries and by up to 7 times for sliding window join continuous queries.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.36 no.11A
• /
• pp.878-891
• /
• 2011

We consider the throughput-maximization problem for both the up- and downlink in a wireless network with interference channels. For this purpose, we design an iterative and distributive uplink algorithm based on Lagrangian relaxation. Using the uplink power prices and network duality, we achieve throughput-maximization in the dual downlink that has a symmetric channel and an equal power budget compared to the uplink. The network duality we prove here is a generalized version of previous research [10], [11]. Computational tests show that the performance of the up- and downlink throughput for our algorithms is close to the optimal value for the channel orthogonality factor, ${\theta}{\in}$(0.5, 1]. On the other hand, when the channels are slightly orthogonal (${\theta}{\in}$(0, 0.5]), we observe some throughput degradation in the downlink. We have extended our analysis to the real downlink that has a nonsymmetric channel and an unequal power budget compared to the uplink. It is shown that the modified duality-based approach is thoroughly applied to the real downlink. Considering the complexity of the algorithms in [6] and [18], we conclude that these results are quite encouraging in terms of both performance and practical applicability of the generalized duality theorem.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.11 no.2
• /
• pp.165-170
• /
• 2016

The characteristic and application of a new duality structure in the $NCV-{\mid}v_1$ > library is studied in this paper. All unitary operations on arbitrarily many qudit's n can be expressed as composition of one- and two-qudit $NCV-{\mid}v_1$ > libraries if their state vectors are eigenvectors. This research provides an extended realization from Barenco's many bits n operator(U(2n)) which is applicable to only all positive polarity statevectors to whole polarity ones. At the control gate synthesis of a unitary operator, such an enhanced expansion is possible due to their symmetric duality property in the case of using both $NCV-{\mid}v_1$ > and $NCV^{\dag}-{\mid}v_1$ > libraries which make the AND predominantly dependent cascade synthesis possible.

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