Characteristic finite element scheme and analysis the three-dimensional two-phase displacement semi-definite problem

NUMERICAL simulation of the two-phase (oil and water) displacement problem is the mathematical basis of energy sources. For two-dimensional positive problem, Douglas et al. put forward the well-known characteristic finite difference method and characteristic finite element method. However, for numerical analysis there exist some difficulties. They assumed that the problem is periodic and the diffusion matrix of the concentration equation is positive difinite

Fairness-Aware Harvested Energy Efficiency Algorithm for IRS-Aided Intelligent Sensor Networks with SWIPT

In this paper,a novel fairness-aware harvested energy efficiency-based green transmission scheme for wireless information and power transfer(SWIPT)aided sensor networks is developed for active beamforming of multiantenna transmitter and passive beamforming at intelligent reflecting surfaces(IRS).By optimizing the active beamformer assignment at the transmitter in conjunction with the passive beamformer assignment at the IRS,we aimtomaximize the minimumharvested energy efficiency among all the energy receivers(ER)where information receivers(IR)are bound to the signal-interference-noise-ratio(SINR)and the maximum transmitted power of the transmitter.To handle the non-convex problem,both semi-definite relaxation(SDR)and block coordinate descent technologies are exploited.Then,the original problem is transformed into two convex sub-problems which can be solved via semidefinite programming.Numerical simulation results demonstrate that the IRS and energy beamformer settings in this paper provide greater system gain than the traditional experimental setting,thereby improving the fairness-aware harvested energy efficiency of the ER.

Performance analysis of ultra-wideband based wireless sensor networks in indoor office LOS environment

By analyzing the indoor office LOS channel model defined by IEEE 802.15.4a standard and deducing the variance for intra-symbol interference (IASI), inter-symbol interference (ISI) and multiuser interference (MUI), performance analysis model for ultra-wideband (UWB) based wireless sensor networks (WSN) is proposed, and the bit error rate (BER) formulation is also obtained. The comparison of performance analysis model with and without intra-symbol interference shows that the intra-symbol interference cannot be neglected and such interference will significantly decrease the system performance. In order to verify the proposed performance analysis model and BER formulation, the semi-definite programming (SDP) algorithm is used to obtain the pulses complying with the spectrum requirement of China and IEEE 802.15.4a standard, and by using such pulses, simulations and theoretical analysis are compared, the comparison results show the validity of the proposed performance analysis model and BER formulation.

Modulus-Based Matrix Splitting Iteration Methods for a Class of Stochastic Linear Complementarity Problem

For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.

Optimal Bounds for the Largest Eigenvalue of a 3 ×3 Correlation Matrix

A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.

Inner Product Laplacian Embedding Based on Semidefinite Programming

This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. The criterion function is to make the neighborhood points on manifold as close as possible while the geodesic distances between those distant points are preserved. The IPLE algorithm sufficiently integrates the advantages of LE, ISOMAP and MVU algorithms. The comparison experiments on two image datasets from COIL-20 images and USPS handwritten digit images are performed by applying LE, ISOMAP, MVU and the proposed IPLE. Experimental results show that the intrinsic low-dimensional coordinates obtained by our algorithm preserve more information according to the fraction of the dominant eigenvalues and can obtain the better comprehensive performance in clustering and manifold structure.

Fuzzy Multi-Objective Semi-Definition Programming

This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming (MSDP), and proposes the fuzzy multi-objective semi-definite programming (FMSDP) model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.

A potential reduction algorithm for an extended SDP problem

An extended semi-definite programming, the SDP with an additional quadratic term in the objective function, is studied. Our generalization is similar to the generalization from linear programming to quadratic programming. Optimal conditions for this new class of problems are discussed and a potential reduction algorithm for solving QSDP problems is presented. The convergence properties of this algorithm are also given.

Second-Order Optimality Conditions for Multiobjective Optimization Whose Order Induced by Second-Order Cone

This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product of second-order cones(here named as Q-multiobjective optimization problem).For an abstract-constrained Q-multiobjective optimization problem,we derive two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions.For Q-multiobjective optimization problem with explicit constraints,we demonstrate first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as second-order sufficient optimality conditions under upper second-order regularity for the explicit constraints.As applications,we obtain optimality conditions for polyhedral conic,second-order conic,and semi-definite conic Q-multiobjective optimization problems.

Linear operators preserving the generalized decomposable numerical range

LET G be a subgroup of the symmetric group Sm. Denote by CG the set of all functions f: G→C. A function f∈CG is said to be positive semi-definite （p. s. d. ） if there exists c∈CG such that for all τ∈G. In particular, the irreducible complex characters of G are p. s. d. Let Cn×m denote the set of all n×m complex matrices. For f∈CG, the

High-order sum-of-squares structured tensors:theory and applications

Tensor decomposition is an important research area with numerous applications in data mining and computational neuroscience.An important class of tensor decomposition is sum-of-squares(SOS)tensor decomposition.SOS tensor decomposition has a close connection with SOS polynomials,and SOS polynomials are very important in polynomial theory and polynomial optimization.In this paper,we give a detailed survey on recent advances of high-order SOS tensors and their applications.It first shows that several classes of symmetric structured tensors available in the literature have SOS decomposition in the even order symmetric case.Then,the SOS-rank for tensors with SOS decomposition and the SOS-width for SOS tensor cones are established.Further,a sharper explicit upper bound of the SOS-rank for tensors with bounded exponent is provided,and the exact SOS-width for the cone consists of all such tensors with SOS decomposition is identified.Some potential research directions in the future are also listed in this paper.

Integrating outlier filtering in large margin training

Large margin classifiers such as support vector machines (SVM) have been applied successfully in various classification tasks.However,their performance may be significantly degraded in the presence of outliers.In this paper,we propose a robust SVM formulation which is shown to be less sensitive to outliers.The key idea is to employ an adaptively weighted hinge loss that explicitly incorporates outlier filtering in the SVM training,thus performing outlier filtering and classification simultaneously.The resulting robust SVM formulation is non-convex.We first relax it into a semi-definite programming which admits a global solution.To improve the efficiency,an iterative approach is developed.We have performed experiments using both synthetic and real-world data.Results show that the performance of the standard SVM degrades rapidly when more outliers are included,while the proposed robust SVM training is more stable in the presence of outliers.

A Cone Constrained Convex Program:Structure and Algorithms

In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and algorithms.We study defining functions,defining sequences and polyhedral outer approximations for this positive semidefinite space tensor cone,give an error bound for the polyhedral outer approximation approach,and thus establish convergence of three polyhedral outer approximation algorithms for solving this problem.We then study some other approaches for solving this structured convex program.These include the conic linear programming approach,the nonsmooth convex program approach and the bi-level program approach.Some numerical examples are presented.

A Note on the Paper “Some Determinantal Inequalities on Complex Positive Definite Matrices”

By presenting a counterexample,the author of paper (ZHAO Li-feng.J.Math.Res.Exposition,2007,27(4): 949–954) declared that some assertions in papers of L Yun-xia,ZHANG Shu-qing (J.Math.Res.Exposition,1999,19(3): 598–600),HE Gan-tong (J.Math.Res.Exposition,2002,22(1): 79–82) and YUAN Hui-ping (J.Math.Res.Exposition,2001,21(3): 464–468) are wrong.In this note,we point out that the counterexample is wrong.Further discussion on these assertions and some related results are also given.