• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.111-123
• /
• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.183-191
• /
• 2007

In this paper, we introduce and study a new class of equilibrium problems, known as regularized mixed quasi equilibrium problems. We use the auxiliary principle technique to suggest and analyze some iterative schemes for regularized equilibrium problems. We prove that the convergence of these iterative methods requires either pseudomonotonicity or partially relaxed strongly monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving equilibrium problems and variational inequalities involving the convex sets.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.743-756
• /
• 2022

We obtained results on upper hemi-continuous and pseudo-monotone type two mappings for sets which are not compact. M.S.R. Chowdhury and K.-K. Tan's improved result on Ky Fan's minimax inequality will be used.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.46 no.5
• /
• pp.8-14
• /
• 2009

In this paper, a convex optimization technique, which is based on the generalized quantization constraint (GQC), is proposed in the compressive sensing reconstruction using quantized measures. The set size of the proposed GQC can be controlled, and through extensive numerical simulations based on the uniform scalar quantizers, the CS reconstruction errors are improved by 3.4-3.6dB compared to the traditional QC method for the CS problems of m/klogn > 2.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.14 no.11
• /
• pp.4595-4610
• /
• 2020

In the practical communication environment, the accurate channel state information (CSI) is difficult to obtain, which will cause the mismatch of resource and degrade the system performance. In this paper, to account for the channel uncertainties, a robust power allocation scheme for a downlink Non-orthogonal multiple access (NOMA) heterogeneous network (HetNet) is designed to maximize energy efficiency (EE), which can ensure the quality of service (QoS) of users. We conduct the robust optimization model based on worse-case method, in which the channel gains belong to certain ellipsoid sets. To solve the non-convex non-liner optimization, we transform the optimization problem via Dinkelbach method and sequential convex programming, and the power allocation of small cell users (SCUs) is achieved by Lagrange dual approach. Finally, we analysis the convergence performance of proposed scheme. The simulation results demonstrate that the proposed algorithm can improve total EE of SCUs, and has a fast convergence performance.

• Journal of the Korean Society for Precision Engineering
• /
• v.15 no.11
• /
• pp.130-136
• /
• 1998

This paper develops an efficient algorithm for the minimum distance calculation between two general polyhedra(convex and/or concave) in three-dimensional space. The polyhedra approximate objects using flat polygons which composed of more than three vertices. The algorithm developed in this paper basically computes minimum distance between two polygons(one polygon per object) and finds a set of two polygons which makes a global minimum distance. The advantage of the algorithm is that the global minimum distance can be computed in any cases. But the big disadvantage is that the minimum distance computing time is rapidly increased with the number of polygons which used to approximate an object. This paper develops a method to eliminate sets of two polygons which have no possibility of minimum distance occurrence, and an efficient algorithm to compute a minimum distance between two polygons in order to compensate the inherent disadvantage of the algorithm. The correctness of the algorithm is verified not only comparing analytically calculated exact minimum distance with one calculated using the developed algorithm but also watching a line which connects two points making a global minimum distance of a convex object and/or a concave object. The algorithm efficiently finds minimum distance between two convex objects made of 224 polygons respectively with a computation time of about 0.1 second.

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.849-856
• /
• 2000

We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.3
• /
• pp.321-326
• /
• 2008

In this note, using the separation theorem for convex sets, we will give a two functions version generalization of Fan's minimax theorem by relaxing the convexlike assumption to the weak convexlike condition.

• Journal of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.243-248
• /
• 2004

In this note, we get some generalized KKM theorems for the k-set contraction mapping on the nearly-convex sets.

• Journal of Broadcast Engineering
• /
• v.16 no.4
• /
• pp.669-679
• /
• 2011

In this paper, we propose a POCS based irregularly sampled image interpolation method exploiting non-local block-based wavelet shrinkage denoising algorithm. The method provides convex sets to improve the performance. The Delaunay triangulation interpolation is first applied to interpolate the missing pixels of the irregularly sampled image into the regular grids. Then, the non-local block-based wavelet shrinkage denoising algorithm is applied, and the originally observed pixels are enforced. After iteration is performed, the denoising algorithm for non-edge areas is applied to acquire the final result. The experimental results show that the proposed method outperforms the conventional methods.