• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.89-106
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• 2022

We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

• Journal of Multimedia Information System
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• v.1 no.1
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• pp.87-93
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• 2014

The aim of microscopic image restoration is to recover the image by applying the inverse process of degradation, and the results facilitate automated and improved analysis of the image. In this work, we consider the problem of image restoration as a minimization problem of convex cost function, which consists of a least-squares fitting term and regularization terms with non-negative constraints. The finite step method is proposed to solve this constrained convex optimization problem. We demonstrate the convergence of this method. Efficiency and restoration capability of the proposed method were tested and illustrated through numerical experiments.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.2
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• pp.3-13
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• 1993

In this study, we develop a B & B type algorithm for the concave minimization problem with 0-1 knapsack constraint. Our algorithm reformulates the original problem into the singly linearly constrained concave minimization problem by relaxing 0-1 integer constraint in order to get a lower bound. But this relaxed problem is the concave minimization problem known as NP-hard. Thus the linear function that underestimates the concave objective function over the given domain set is introduced. The introduction of this function bears the following important meanings. Firstly, we can efficiently calculate the lower bound of the optimal object value using the conventional convex optimization methods. Secondly, the above linear function like the concave objective function generates the vertices of the relaxed solution set of the subproblem, which is used to update the upper bound. The fact that the linear underestimating function is uniquely determined over a given simplex enables us to fix underestimating function by considering the simplex containing the relaxed solution set. The initial containing simplex that is the intersection of the linear constraint and the nonnegative orthant is sequentially partitioned into the subsimplices which are related to subproblems.

• Journal of the Korea Convergence Society
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• v.7 no.5
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• pp.213-219
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• 2016

This paper presents a branch-and-bound algorithm for solving the concave minimization problem with upper bounded variables whose single constraint is linear. The algorithm uses simplex as partition element. Because the convex envelope which most tightly underestimates the concave function on the simplex is uniquely determined by solving the related linear equations. Every branching process generates two subsimplices one lower dimensional than the candidate simplex by adding 0 and upper bound constraints. Subsequently the feasible points are partitioned into two sets. During the bounding process, the linear programming problems defined over subsimplices are minimized to calculate the lower bound and to update the incumbent. Consequently the simplices which do certainly not contain the global minimum are excluded from consideration. The major advantage of the algorithm is that the subproblems are defined on the one less dimensinal space. It means that the amount of work required for the subproblem decreases whenever the branching occurs. Our approach can be applied to solving the concave minimization problems under knapsack type constraints.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.451-474
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• 2021

In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.12
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• pp.5614-5633
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• 2018

Mobile Edge Computing (MEC) and Wireless Power Transfer (WPT) are both recognized as promising techniques, one is for solving the resource insufficient of mobile devices and the other is for powering the mobile device. Naturally, by integrating the two techniques, task will be capable of being executed by the harvested energy which makes it possible that less intrinsic energy consumption for task execution. However, this innovative integration is facing several challenges inevitably. In this paper, we aim at prolonging the battery life of mobile device for which we need to maximize the harvested energy and minimize the consumed energy simultaneously, which is formulated as residual energy maximization (REM) problem where the offloading ratio, energy harvesting time, CPU frequency and transmission power of mobile device are all considered as key factors. To this end, we jointly optimize the offloading ratio, energy harvesting time, CPU frequency and transmission power of mobile device to solve the REM problem. Furthermore, we propose an efficient convex optimization and sequential unconstrained minimization technique based combining method to solve the formulated multi-constrained nonlinear optimization problem. The result shows that our joint optimization outperforms the single optimization on REM problem. Besides, the proposed algorithm is more efficiency.

• ETRI Journal
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• v.39 no.1
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• pp.13-20
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• 2017

A method is proposed for scheduling sensor accesses to the shared network in a networked control system. The proposed method determines the access order in which the sensors are granted medium access through minimization of the state estimation error covariance. Solving the problem by evaluating the error covariance for each possible ordered set of sensors is not practical for large systems. Therefore, a convex optimization problem is proposed, which yields approximate yet acceptable results. A state estimator is designed for the augmented system resulting from the incorporation of the optimally chosen communication sequence in the plant dynamics. A car suspension system simulation is conducted to test the proposed method. The results show promising improvement in the state estimation performance by reducing the estimation error norm compared to round-robin scheduling.

• Journal of Communications and Networks
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• v.18 no.2
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• pp.173-181
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• 2016

In this paper, we address a new robust optimization problem in a multiuser multiple-input single-output broadcasting system with simultaneous wireless information and power transmission, where a multi-antenna base station (BS) sends energy and information simultaneously to multiple users equipped with a single antenna. Assuming that perfect channel-state information (CSI) for all channels is not available at the BS, the uncertainty of the CSI is modeled by an Euclidean ball-shaped uncertainty set. To optimally design transmit beamforming weights and receive power splitting, an average total transmit power minimization problem is investigated subject to the individual harvested power constraint and the received signal-to-interference-plus-noise ratio constraint at each user. Due to the channel uncertainty, the original problem becomes a homogeneous quadratically constrained quadratic problem, which is NP-hard. The original design problem is reformulated to a relaxed semidefinite program, and then two different approaches based on convex programming are proposed, which can be solved efficiently by the interior point algorithm. Numerical results are provided to validate the robustness of the proposed algorithms.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.423-438
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• 2017

The aim of this paper is to present two new viscosity rules for nonexpansive mappings in Hilbert spaces. Under some assumptions, the strong convergence theorems of the purposed new viscosity rules are proved. Some applications are also included.

• Journal of Communications and Networks
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• v.16 no.1
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• pp.36-44
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• 2014

Exploiting the energy-delay tradeoff for energy saving is critical for developing green wireless communication systems. In this paper, we investigate the delay-constrained energy-efficient packet transmission. We aim to minimize the energy consumption of multiple randomly arrived packets in an additive white Gaussian noise channel subject to individual packet delay constraints, by taking into account the practical on-off circuit power consumption at the transmitter. First, we consider the offline case, by assuming that the full packet arrival information is known a priori at the transmitter, and formulate the energy minimization problem as a non-convex optimization problem. By exploiting the specific problem structure, we propose an efficient scheduling algorithm to obtain the globally optimal solution. It is shown that the optimal solution consists of two types of scheduling intervals, namely "selected-off" and "always-on" intervals, which correspond to bits-per-joule energy efficiency maximization and "lazy scheduling" rate allocation, respectively. Next, we consider the practical online case where only causal packet arrival information is available. Inspired by the optimal offline solution, we propose a new online scheme. It is shown by simulations that the proposed online scheme has a comparable performance with the optimal offline one and outperforms the design without considering on-off circuit power as well as the other heuristically designed online schemes.