• Journal of applied mathematics & informatics
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• 제13권1_2호
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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.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.475-489
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• 2022

This paper focuses on a robust semi-infinite interval-valued optimization problem with uncertain inequality constraints (RSIIVP). By employing the concept of LU-optimal solution and Extended Mangasarian-Fromovitz Constraint Qualification (EMFCQ), necessary optimality conditions are established for (RSIIVP) and then sufficient optimality conditions for (RSIIVP) are derived, by using the tools of convexity. Moreover, a Wolfe type dual problem for (RSIIVP) is formulated and usual duality results are discussed between the primal (RSIIVP) and its dual (RSIWD) problem. The presented results are demonstrated by non-trivial examples.

• 한국경영과학회지
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• 제13권2호
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• pp.9-17
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• 1988

This vehicle scheduling problem with multiple depots and multiple vehicle types (VMM) is to determine the optimal vehicle routes to minimize the total travel costs. The object of this paper is to develope an exact algorithm for the VMM. In this paper the VMM is transformed into a mathematical model of the vehicle problem with multiple depots. Then an efficient branch and bound algorithm is developed to obtain an exact solution for this model. In order to enhance the efficiency, this algorithm emphasizes the follows; First, a heuristic algorithm is developed to get a good initial upper bound. Second, an primal-dual approach is used to solve subproblems which are called the quasi-assignment problem, formed by branching strategy is presented to reduce the number of the candidate subproblems.

• Kyungpook Mathematical Journal
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• 제51권4호
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• pp.353-364
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• 2011

Duality in the optimal harvesting for a nonlinear age-spatial structured population dynamic model is studied in the framework of optimal control problem. In this paper the duality theory that displays the conjugacy of the primal problem is established and an application is given. Duality theory plays an important role in both optimization theory and methodology and the results may be applied to a realistic biological system on the point of optimal harvesting.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.1-10
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• 2003

In this paper, we establish a nonlinear Lagrangian algorithm for nonlinear programming problems with inequality constraints. Under some assumptions, it is proved that the sequence of points, generated by solving an unconstrained programming, convergents locally to a Kuhn-Tucker point of the primal nonlinear programming problem.

• Journal of Electrical Engineering and Technology
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• 제6권6호
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• pp.786-792
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• 2011

The present paper presents an optimal capacitor placement (OCP) algorithm for voltagestability enhancement. The OCP issue is represented using a mixed-integer problem and a highly nonlinear problem. The hybrid particle swarm optimization (HPSO) algorithm is proposed to solve the OCP problem. The HPSO algorithm combines the optimal power flow (OPF) with the primal-dual interior-point method (PDIPM) and ordinary PSO. It takes advantage of the global search ability of PSO and the very fast simulation running time of the OPF algorithm with PDIPM. In addition, OPF gives intelligence to PSO through the information provided by the dual variable of the OPF. Numerical results illustrate that the HPSO algorithm can improve the accuracy and reduce the simulation running time. Test results evaluated with the three-bus, New England 39-bus, and Korea Electric Power Corporation systems show the applicability of the proposed algorithm.

• 한국경영과학회지
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• 제14권1호
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• pp.16-26
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• 1989

The terminal layout problem is fundamental in may centralized computer networks, which is generated formulated as the capaciated minimum spanning tree problem (CMSTP). We present an implementation of the dual-based procedure to solve the CMSTP. Dual ascent procedure generates a good feasible solutions to the dual of the linear programming relaxation of CMSTP. A feasible primal solution to CMSTP can then be constructed based on this dual solution. This procedure can be used either as a stand-alone heuristic or, else, it can be incorporated into a branch and bound algorithm. A numerical result is given with quite favorable results.

• 대한수학회지
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• 제47권1호
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• pp.17-28
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• 2010

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

• Journal of Communications and Networks
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• 제13권6호
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• pp.633-638
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• 2011

In this paper, we consider resource allocation with proportional fairness in the downlink orthogonal frequency division multiple access relay networks, in which relay nodes operate in decode-and-forward mode. A joint optimization problem is formulated for relay selection, subcarrier assignment and power allocation. Since the formulated primal problem is nondeterministic polynomial time-complete, we make continuous relaxation and solve the dual problem by Lagrangian dual decomposition method. A near-optimal solution is obtained using Karush-Kuhn-Tucker conditions. Simulation results show that the proposed algorithm provides superior system throughput and much better fairness among users comparing with a heuristic algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제7권2호
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• pp.288-307
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• 2013

This paper formulates resource allocation for decode-and-forward (DF) relay assisted multi-cell orthogonal frequency division multiple (OFDM) networks as an optimization problem taking into account of inter-cell interference and users fairness. To maximize the transmit rate of system we propose a joint interference coordination, subcarrier and power allocation algorithm. To reduce the complexity, this semi-distributed algorithm divides the primal optimization into three sub-optimization problems, which transforms the mixed binary nonlinear programming problem (BNLP) into standard convex optimization problems. The first layer optimization problem is used to get the optimal subcarrier distribution index. The second is to solve the problem that how to allocate power optimally in a certain subcarrier distribution order. Based on the concept of equivalent channel gain (ECG) we transform the max-min function into standard closed expression. Subsequently, with the aid of dual decomposition, water-filling theorem and iterative power allocation algorithm the optimal solution of the original problem can be got with acceptable complexity. The third sub-problem considers dynamic co-channel interference caused by adjacent cells and redistributes resources to achieve the goal of maximizing system throughput. Finally, simulation results are provided to corroborate the proposed algorithm.