A New Infeasible Interior-point Method for Linear Complementarity Problem Based on Full Newton Step

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last,we prove that the algorithm has O(nlog n/ε) polynomial complexity,which coincides with the best known one for the infeasible interior-point algorithm at present.

A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming

In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.

A NEW FRAMEWORK OF PRIMAL-DUAL INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR PROGRAMMING

On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.

Interior-Point Methods Applied to the Predispatch Problem of a Hydroelectric System with Scheduled Line Manipulations

Transmission line manipulations in a power system are necessary for the execution of preventative or corrective main- tenance in a network, thus ensuring the stability of the system. In this study, primal-dual interior-point methods are used to minimize costs and losses in the generation and transmission of the predispatch active power flow in a hydroelectric system with previously scheduled line manipulations for preventative maintenance, over a period of twenty-four hours. The matrix structure of this problem and the modification that it imposes on the system is also broached in this study. From the computational standpoint, the effort required to solve a problem with or without line manipulations is similar, and the reasons for this are also discussed in this study. Computational results sustain our findings.

A NEWTON-TYPE GLOBALLY CONVERGENT INTERIOR-POINT METHOD TO SOLVE MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

This paper proposes an interior-point technique for detecting the nondominated points of multi-objective optimization problems using the direction-based cone method.Cone method decomposes the multi-objective optimization problems into a set of single-objective optimization problems.For this set of problems,parametric perturbed KKT conditions are derived.Subsequently,an interior point technique is developed to solve the parametric perturbed KKT conditions.A differentiable merit function is also proposed whose stationary point satisfies the KKT conditions.Under some mild assumptions,the proposed algorithm is shown to be globally convergent.Numerical results of unconstrained and constrained multi-objective optimization test problems are presented.Also,three performance metrics(modified generational distance,hypervolume,inverted generational distance)are used on some test problems to investigate the efficiency of the proposed algorithm.We also compare the results of the proposed algorithm with the results of some other existing popular methods.

Insight Into the Separation-of-Variable Methods for the Closed-Form Solutions of Free Vibration of Rectangular Thin Plates

The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.

Structural Modal Parameter Recognition and Related Damage Identification Methods under Environmental Excitations: A Review

Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.

A Kernel Function Based Interior-Point Methods for Solving P_*(κ)-Linear Complementarity Problem

In this paper, motivated by the complexity results of Interior Point Methods （IPMs） for Linear Optimization （LO） based on kernel functions, we present a polynomial time IPM for solving P.（a）-linear complementarity problem, using a new class of kernel functions. The special case of our new class was considered earlier for LO by Y. Q. Bai et al. in 2004. Using some appealing properties of the new class, we show that the iteration bound for IPMs matches the so far best known theoretical iteration bound for both large and small updates by choosing special values for the parameters of the new class.

Sparse Proximal Support Vector Machine with a Specialized Interior-Point Method

Support vector machine(SVM)is a widely used method for classification.Proximal support vector machine(PSVM)is an extension of SVM and a promisingmethod to lead to a fast and simple algorithm for generating a classifier.Motivated by the fast computational efforts of PSVM and the properties of sparse solution yielded by l1-norm,in this paper,we first propose a PSVM with a cardinality constraint which is eventually relaxed byl1-norm and leads to a trade-offl1−l2 regularized sparse PSVM.Next we convert thisl1−l2 regularized sparse PSVM into an equivalent form of1 regularized least squares(LS)and solve it by a specialized interior-point method proposed by Kim et al.(J SelTop Signal Process 12:1932–4553,2007).Finally,l1−l2 regularized sparse PSVM is illustrated by means of a real-world dataset taken from the University of California,Irvine Machine Learning Repository(UCI Repository).Moreover,we compare the numerical results with the existing models such as generalized eigenvalue proximal SVM(GEPSVM),PSVM,and SVM-Light.The numerical results showthat thel1−l2 regularized sparsePSVMachieves not only better accuracy rate of classification than those of GEPSVM,PSVM,and SVM-Light,but also a sparser classifier compared with the1-PSVM.

Bio-inspired heuristics hybrid with interior-point method for active noise control systems without identification of secondary path

In this study, hybrid computational frameworks are developed for active noise control（ANC） systems using an evolutionary computing technique based on genetic algorithms（GAs） and interior-point method（IPM）, following an integrated approach, GA-IPM. Standard ANC systems are usually implemented with the filtered extended least mean square algorithm for optimization of coefficients for the linear finite-impulse response filter, but are likely to become trapped in local minima（LM）. This issue is addressed with the proposed GA-IPM computing approach which is considerably less prone to the LM problem. Also, there is no requirement to identify a secondary path for the ANC system used in the scheme. The design method is evaluated using an ANC model of a headset with sinusoidal, random, and complex random noise interferences under several scenarios based on linear and nonlinear primary and secondary paths. The accuracy and convergence of the proposed scheme are validated based on the results of statistical analysis of a large number of independent runs of the algorithm.

A Class of Path-Following Interior-Point Methods for P_(∗)(κ)-Horizontal Linear Complementarity Problems

In this paper,a class of polynomial interior-point algorithms for P_(∗)(κ)-horizontal linear complementarity problems based on a newparametric kernel function is presented.The new parametric kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center of the problem.We derive the complexity analysis for the algorithm,both with large and small updates.

A Modified and Simplified Full Nesterov–Todd Step O(N)Infeasible Interior-Point Method for Second-Order Cone Optimization

We present a modified and simplified version of an infeasible interior-point method for second-order cone optimization published in 2013(Zangiabadi et al.in J Optim Theory Appl,2013).In the earlier version,each iteration consisted of one socalled feasibility step and a few centering steps.Here,each iteration consists of only a feasibility step.Thus,the new algorithm improves the number of iterations and the improvement is due to a lemma which gives an upper bound for the proximity after the feasibility step.The complexity result coincides with the best-known iteration bound for infeasible interior-point methods.

Kernel Function-Based Primal-Dual Interior-Point Methods for Symmetric Cones Optimization

In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.

A Wide Neighborhood Interior-Point Method for Cartesian P_(∗)(κ)-LCP over Symmetric Cones

this paper,we propose an infeasible-interior-point method,based on a new wide neighborhood of the central path,for linear complementarity problems over symmetric cones with the Cartesian P_(∗)(κ)-property.The convergence is shown for commutative class of search directions.Moreover,we analyze the algorithm and obtain the complexity bounds,which coincide with the best-known results for the Cartesian P_(∗)(κ)-SCLCPs.Some numerical tests are reported to illustrate our theoretical results.

A Review on Sources,Extractions and Analysis Methods of a Sustainable Biomaterial:Tannins

Condensed and hydrolysable tannins are non-toxic natural polyphenols that are a commercial commodity industrialized for tanning hides to obtain leather and for a growing number of other industrial applications mainly to substitute petroleum-based products.They are a definite class of sustainable materials of the forestry industry.They have been in operation for hundreds of years to manufacture leather and now for a growing number of applications in a variety of other industries,such as wood adhesives,metal coating,pharmaceutical/medical applications and several others.This review presents the main sources,either already or potentially commercial of this forestry by-materials,their industrial and laboratory extraction systems,their systems of analysis with their advantages and drawbacks,be these methods so simple to even appear primitive but nonetheless of proven effectiveness,or very modern and instrumental.It constitutes a basic but essential summary of what is necessary to know of these sustainable materials.In doing so,the review highlights some of the main challenges that remain to be addressed to deliver the quality and economics of tannin supply necessary to fulfill the industrial production requirements for some materials-based uses.

A Primal-Dual Interior-Point Method for Optimal Grasping Manipulation of Multi-fingered Hand-Arm Robots

In this paper,we consider an optimization problem of the grasping manipulation of multi-fingered hand-arm robots.We first formulate an optimization model for the problem,based on the dynamic equations of the object and the friction constraints.Then,we reformulate the model as a convex quadratic programming over circular cones.Moreover,we propose a primal-dual interior-point algorithm based on the kernel function to solve this convex quadratic programming over circular cones.We derive both the convergence of the algorithm and the iteration bounds for largeand small-update methods,respectively.Finally,we carry out the numerical tests of 180◦and 90◦manipulations of the hand-arm robot to demonstrate the effectiveness of the proposed algorithm.

A comparison study on structure-function relationship of polysaccharides obtained from sea buckthorn berries using different methods:antioxidant and bile acid-binding capacity

In this study,the structural characters,antioxidant activities and bile acid-binding ability of sea buckthorn polysaccharides(HRPs)obtained by the commonly used hot water(HRP-W),pressurized hot water(HRP-H),ultrasonic(HRP-U),acid(HRP-C)and alkali(HRP-A)assisted extraction methods were investigated.The results demonstrated that extraction methods had significant effects on extraction yield,monosaccharide composition,molecular weight,particle size,triple-helical structure,and surface morphology of HRPs except for the major linkage bands.Thermogravimetric analysis showed that HRP-U with filamentous reticular microstructure exhibited better thermal stability.The HRP-A with the lowest molecular weight and highest arabinose content possessed the best antioxidant activities.Moreover,the rheological analysis indicated that HRPs with higher galacturonic acid content and molecular weight showed higher viscosity and stronger crosslinking network(HRP-C,HRP-W and HRP-U),which exhibited stronger bile acid binding capacity.The present findings provide scientific evidence in the preparation technology of sea buckthorn polysaccharides with good antioxidant and bile acid binding capacity which are related to the structure affected by the extraction methods.

Drilling-based measuring method for the c-φ parameter of rock and its field application

The technology of drilling tests makes it possible to obtain the strength parameter of rock accurately in situ. In this paper, a new rock cutting analysis model that considers the influence of the rock crushing zone(RCZ) is built. The formula for an ultimate cutting force is established based on the limit equilibrium principle. The relationship between digital drilling parameters(DDP) and the c-φ parameter(DDP-cφ formula, where c refers to the cohesion and φ refers to the internal friction angle) is derived, and the response of drilling parameters and cutting ratio to the strength parameters is analyzed. The drillingbased measuring method for the c-φ parameter of rock is constructed. The laboratory verification test is then completed, and the difference in results between the drilling test and the compression test is less than 6%. On this basis, in-situ rock drilling tests in a traffic tunnel and a coal mine roadway are carried out, and the strength parameters of the surrounding rock are effectively tested. The average difference ratio of the results is less than 11%, which verifies the effectiveness of the proposed method for obtaining the strength parameters based on digital drilling. This study provides methodological support for field testing of rock strength parameters.

Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.

Material point method simulation of hydro-mechanical behaviour in twophase porous geomaterials: A state-of-the-art review

The material point method(MPM)has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformation.In this paper,we survey the current state-of-the-art in the MPM simulation of hydro-mechanical behaviour in two-phase porous geomaterials.The review covers the recent advances and developments in the MPM and their extensions to capture the coupled hydro-mechanical problems involving large deformations.The focus of this review is aiming at providing a clear picture of what has or has not been developed or implemented for simulating two-phase coupled large deformation problems,which will provide some direct reference for both practitioners and researchers.