A dai-liao hybrid conjugate gradient method for unconstrained optimization

One of todays’ best-performing CG methods is Dai-Liao (DL) method which depends on non-negative parameter  and conjugacy conditions for its computation. Although numerous optimal selections for the parameter were suggested, the best choice of  remains a subject of consideration. The pure conjugacy condition adopts an exact line search for numerical experiments and convergence analysis. Though, a practical mathematical experiment implies using an inexact line search to find the step size. To avoid such drawbacks, Dai and Liao substituted the earlier conjugacy condition with an extended conjugacy condition. Therefore, this paper suggests a new hybrid CG that combines the strength of Liu and Storey and Conjugate Descent CG methods by retaining a choice of Dai-Liao parameterthat is optimal. The theoretical analysis indicated that the search direction of the new CG scheme is descent and satisfies sufficient descent condition when the iterates jam under strong Wolfe line search. The algorithm is shown to converge globally using standard assumptions. The numerical experimentation of the scheme demonstrated that the proposed method is robust and promising than some known methods applying the performance profile Dolan and Mor´e on 250 unrestricted problems.  Numerical assessment of the tested CG algorithms with sparse signal reconstruction and image restoration in compressive sensing problems, file restoration, image video coding and other applications. The result shows that these CG schemes are comparable and can be applied in different fields such as temperature, fire, seismic sensors, and humidity detectors in forests, using wireless sensor network techniques

Two new Hager–Zhang iterative schemes with improved parameter choices for monotone nonlinear systems and their applications in compressed sensing

Notwithstanding its efficiency and nice attributes, most research on the Hager–Zhang (HZ) iterative scheme are focused on unconstrained minimization problems. Inspired by this and recent extensions of the one-parameter HZ scheme to system of nonlinear monotone equations, two new HZ-type iterative methods are developed in this paper for solving system of monotone equations with convex constraint. This is achieved by developing two HZ-type search directions with new parameter choices combined with the popular projection method. The first parameter choice is obtained by minimizing the condition number of a modified HZ direction matrix, while the second choice is realized using singular value analysis and minimizing the spectral condition number of a nonsingular HZ search direction matrix. Interesting properties of the schemes include solving non-smooth problems and satisfying the inequality that is vital for global convergence. Using standard assumptions, global convergence of the schemes are proven and numerical experiments with recent methods in the literature, indicate that the methods proposed are promising. The effectiveness of the schemes are further demonstrated by their applications to sparse signal and image reconstruction problems, where they outperform some recent schemes in the literature

Hybrid derivative-free methods for solving system of nonlinear equations

This work presents a predictor-corrector iterative approach for solving systems of nonlinear equations. The methods are derivative-free with correction and acceleration parameters obtained via approximating the Jacobian matrix. Using an inexact line search procedure and under appropriate conditions, we proved that the proposed method is globally convergent. We, additionally, present some numerical results to show the efficiency and effectiveness of the proposed method

Reduction of Mutual Coupling in UWB/MIMO Antenna using Stub Loading Technique

The research presents mutual coupling reduction between UWB-MIMO antenna elements using stub loading technique. The proposed 2 × 2 UWB antenna geometry consists of two circular-shaped monopole radiators with a partial ground for perfect impedance matching. Stubs of 20 mm × 0.2 mm areinserted between the two antenna elements in the ground plane to improve the isolation. The decoupling stub leads to a mutual coupling reduction of less than 20 dB. The farfield measurement at a selected frequency of 10 GHz confirms an omnidirectional radiation pattern. Different MIMO antenna metric such as channel capacity loss (CCL), mean effective gain (MEG), total active reflection coefficient (TARC), envelope correlationcoefficient (ECC), and surface current are presented. Details of the design considerations and the simulation and measurement results are presented and discussed. The proposed MIMO antenna array can be well suited for UWB applications

Reduction of Mutual Coupling in UWB/MIMO Antenna Using Stub Loading Technique

The research presents mutual coupling reduction between UWB-MIMO antenna elements using stub loading technique. The proposed 2 × 2 UWB antenna geometry consists of two circular-shaped monopole radiators with a partial ground for perfect impedance matching. Stubs of 20 mm × 0.2 mm are inserted between the two antenna elements in the ground plane to improve the isolation. The decoupling stub leads to a mutual coupling reduction of less than 20 dB. The farfield measurement at a selected frequency of 10 GHz confirms an omnidirectional radiation pattern. Different MIMO antenna metric such as channel capacity loss (CCL), mean effective gain (MEG), total active reflection coefficient (TARC), envelope correlation coefficient (ECC), and surface current are presented. Details of the design considerations and the simulation and measurement results are presented and discussed. The proposed MIMO antenna array can be well suited for UWB applications

Descent Derivative-Free Method Involving Symmetric Rank-One Update for Solving Convex Constrained Nonlinear Monotone Equations and Application to Image Recovery

Many practical applications in applied sciences such as imaging, signal processing, and motion control can be reformulated into a system of nonlinear equations with or without constraints. In this paper, a new descent projection iterative algorithm for solving a nonlinear system of equations with convex constraints is proposed. The new approach is based on a modified symmetric rank-one updating formula. The search direction of the proposed algorithm mimics the behavior of a spectral conjugate gradient algorithm where the spectral parameter is determined so that the direction is sufficiently descent. Based on the assumption that the underlying function satisfies monotonicity and Lipschitz continuity, the convergence result of the proposed algorithm is discussed. Subsequently, the efficiency of the new method is revealed. As an application, the proposed algorithm is successfully implemented on image deblurring problem

Descent Derivative-Free Method Involving Symmetric Rank-One Update for Solving Convex Constrained Nonlinear Monotone Equations and Application to Image Recovery

Many practical applications in applied sciences such as imaging, signal processing, and motion control can be reformulated into a system of nonlinear equations with or without constraints. In this paper, a new descent projection iterative algorithm for solving a nonlinear system of equations with convex constraints is proposed. The new approach is based on a modified symmetric rank-one updating formula. The search direction of the proposed algorithm mimics the behavior of a spectral conjugate gradient algorithm where the spectral parameter is determined so that the direction is sufficiently descent. Based on the assumption that the underlying function satisfies monotonicity and Lipschitz continuity, the convergence result of the proposed algorithm is discussed. Subsequently, the efficiency of the new method is revealed. As an application, the proposed algorithm is successfully implemented on image deblurring problem

Electroencephalogram (EEG) Based Imagined Speech Decoding and Recognition

The recent investigations and advances in imagined speech decoding and recognition has tremendously improved the decoding of speech directly from brain activity with the help of several neuroimaging techniques that assist us in exploring the neurological processes of imagined speech. This development leads to assist people with disabilities to benefit from neuroprosthetic devices that improve the life of those suffering from neurological disorders. This paper presents the summary of recent progress in decoding imagined speech using Electroenceplography (EEG) signal, as this neuroimaging method enable us to monitor brain activity with high temporal resolution, it is very portable, low cost, and safer as compared to other methods. Therefore, it is a good candidate in investigating an imagined speech decoding from the human cortex which remains a challenging task. The paper also reviews some recent techniques, challenges, future recommendations and possible solutions to improve prosthetic devices and the development of brain computer interface system (BCI)

A Review on Optimal Siting and Sizing of DSTATCOM

The continuous demand for electrical energy by industries and domestic users have stressed the electricity consumption to a high level. Because most components of domestic and industrial systems are made of power electronics devices in their designs. In addition, modern electrical power distribution networks (DNs) are subjected to major disturbances. Consequently, today’s power system is laden with power quality problems such as excessive energy losses, voltage deviations, poor power factor (PF), voltage instability and reliability issues to mentioned just a few. To forestall these disturbances, Distribution Engineers have introduced the use of Custom Power Devices (CPDs) in order to reduce power losses so as improve power quality. Amongst CPDs, Distribution Static Compensator (D-STATCOM) proves most promising in minimizing power quality issues because it generates minimal harmonics, waste less power, has small size, high regulatory capability and cost effective. Researchers in recent years have focused on methodologies required for identifying the most suitable location and rating of D- STATCOM device based on divergent views. However, to date, only one author has so far reviewed a paper on this aspect of study. This paper discusses the latest study on appropriate installation and rating of D-STATCOM techniques for balanced and unbalanced radial distribution networks (UBRDNs). The paper has also provided a comprehensive literature study on the location of DSTATCOM in RDNs for power loss reduction and power quality enhancement. Comparative analyses of various techniques for development of DSTATCOM Objective functions and constraints; Merits and Demerits are presented