• Journal of applied mathematics & informatics
• /
• v.31 no.5_6
• /
• pp.835-852
• /
• 2013

In this paper, we have considered a class of constrained non-smooth multiobjective fractional programming problem involving support functions under generalized convexity. Also, second order Mond Weir type dual and Schaible type dual are discussed and various weak, strong and strict converse duality results are derived under generalized class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions. Also, we have illustrated through non-trivial examples that class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions extends the definitions of generalized convexity appeared in the literature.

• ETRI Journal
• /
• v.36 no.3
• /
• pp.506-509
• /
• 2014

This paper studies the energy efficiency power allocation for cognitive radio networks based on uplink orthogonal frequency-division multiplexing. The power allocation problem is intended to minimize the maximum energy efficiency measured by "Joule per bit" metric, under total power constraint and robust aggregate mutual interference power constraint. However, the above problem is non-convex. To make it solvable, an equivalent convex optimization problem is derived that can be solved by general fractional programming. Then, a robust energy efficiency power allocation scheme is presented. Simulation results corroborate the effectiveness of the proposed methods.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1991.10a
• /
• pp.3-3
• /
• 1991

• ETRI Journal
• /
• v.37 no.3
• /
• pp.471-479
• /
• 2015

Traditional designs of cognitive radio (CR) focus on maximizing system throughput. In this paper, we study the joint overlay and underlay power allocation problem for orthogonal frequency-division multiple access-based CR. Instead of maximizing system throughput, we aim to maximize system energy efficiency (EE), measured by a "bit per Joule" metric, while maintaining the minimal rate requirement of a given CR system, under the total power constraint of a secondary user and interference constraints of primary users. The formulated energy-efficient power allocation (EEPA) problem is nonconvex; to make it solvable, we first transform the original problem into a convex optimization problem via fractional programming, and then the Lagrange dual decomposition method is used to solve the equivalent convex optimization problem. Finally, an optimal EEPA allocation scheme is proposed. Numerical results show that the proposed method can achieve better EE performance.

• Journal of the Korean Mathematical Society
• /
• v.41 no.5
• /
• pp.821-864
• /
• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• Management Science and Financial Engineering
• /
• v.7 no.2
• /
• pp.59-71
• /
• 2001

In the present paper, we present method to solve a Fractional Bulk Transportation Problem(FBTP) in which the numerator is quadratic in nature and the denominator is linear. A related (FBTP) is formed whose feasible solutions are ranked to reach an optimal solution of the given problem. The method to find these feasible solutions makes use of parametric programming wherein a series of Ordinary Bulk Transportation Problems are solved by the usual methods.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.9 no.11
• /
• pp.4387-4404
• /
• 2015

The energy-efficient design of sensing-based spectrum sharing of a multi-input and multi-output (MIMO) cognitive radio (CR) system with imperfect multiple antenna spectrum sensing is investigated in this study. Optimal resource allocation strategies, including sensing time and power allocation schemes, are studied to maximize the energy efficiency (EE) of the secondary base station under the transmit power and interference power constraints. EE problem is formulated as a nonlinear stochastic fractional programming of a nonconvex optimal problem. The EE problem is transformed into its equivalent nonlinear parametric programming and solved by one-dimension search algorithm. To reduce searching complexity, the search range was founded by demonstration. Furthermore, simulation results confirms that an optimal sensing time exists to maximize EE, and shows that EE is affected by the spectrum detection factors and corresponding constraints.

• ETRI Journal
• /
• v.36 no.4
• /
• pp.686-689
• /
• 2014

This paper studies energy-efficiency (EE) power allocation for cognitive radio MIMO-OFDM systems. Our aim is to minimize energy efficiency, measured by "Joule per bit" metric, while maintaining the minimal rate requirement of a secondary user under a total power constraint and mutual interference power constraints. However, since the formulated EE problem in this paper is non-convex, it is difficult to solve directly in general. To make it solvable, firstly we transform the original problem into an equivalent convex optimization problem via fractional programming. Then, the equivalent convex optimization problem is solved by a sequential quadratic programming algorithm. Finally, a new iterative energy-efficiency power allocation algorithm is presented. Numerical results show that the proposed method can obtain better EE performance than the maximizing capacity algorithm.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.13 no.3
• /
• pp.1325-1344
• /
• 2019

Recently, to satisfy mobile users' increasing data transmission requirement, energy efficiency (EE) resource allocation in distributed antenna systems (DASs) has become a hot topic. In this paper, we aim to maximize EE in DASs subject to constraints of the minimum data rate requirement and the maximum transmission power of distributed antenna units (DAUs) with different density distributions. Virtual cell is defined as DAUs selected by the same user equipment (UE) and the size of virtual cells is dependent on the number of subcarriers and the transmission power. Specifically, the selection rule of DAUs is depended on different scenarios. We develop two scenarios based on the density of DAUs, namely, the sparse scenario and the dense scenario. In the sparse scenario, each DAU can only be selected by one UE to avoid co-channel interference. In order to make the original non-convex optimization problem tractable, we transform it into an equivalent fractional programming and solve by the following two sub-problems: optimal subcarrier allocation to find suitable DAUs; optimal power allocation for each subcarrier. Moreover, in the dense scenario, we consider UEs could access the same channel and generate co-channel interference. The optimization problem could be transformed into a convex form based on interference upper bound and fractional programming. In addition, an energy-efficient DAU selection scheme based on the large scale fading is developed to maximize EE. Finally, simulation results demonstrate the effectiveness of the proposed algorithm for both sparse and dense scenarios.

• Genomics & Informatics
• /
• v.1 no.1
• /
• pp.25-31
• /
• 2003

Local alignment is an important task in molecular biology to see if two sequences contain regions that are similar. The most popular approach to local alignment is the use of dynamic programming due to Smith and Waterman, but the alignment reported by the Smith-Waterman algorithm has some undesirable properties. The recent approach to fix these problems is to use the notion of normalized scores for local alignments by Arslan, Egecioglu and Pevzner. In this paper we consider the problem of finding all local alignments whose normalized scores are above a given threshold, and present a fast heuristic algorithm. Our algorithm is 180-330 times faster than Arslan et al.'s for sequences of length about 120 kbp and about 40-50 times faster for sequences of length about 30 kbp.