EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.

A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems

We establish that the generalized Fischer-Burmeister（FB） function and penalized Generalized Fischer-Burmeister （FB） function defined on symmetric cones are complementarity functions （C-functions）, in terms of Euclidean Jordan algebras, and the Generalized Fischer-Burmeister complementarity function for the symmetric cone complementarity problem （SCCP）. It provides an affirmative answer to the open question by Kum and Lim （Kum S H, Lim Y. Penalized complementarity functions on symmetric cones. J. Glob. Optim.. 2010, 46： 475-485） for any positive integer.

Merit functions for nonsmooth complementarity problems and related descent algorithm

Under some assumptions, the solution set of a nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. This paper uses a family of new merit functions to deal with nonlinear complementarity problem where the underlying function is assumed to be a continuous but not necessarily locally Lipschitzian map and gives a descent algorithm for solving the nonsmooth continuous complementarity problems. In addition, the global convergence of the derivative free descent algorithm is also proved.

A New Class of Complementarity Function and the Boundedness of Its Merit Function for Symmetric Cone Complementarity Problem

In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions(C-function). Moreover, its merit function has bounded level set under a weak condition.

Interior-point algorithm based on general kernel function for monotone linear complementarity problem

A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.

Filter-sequence of quadratic programming method with nonlinear complementarity problem function

A mechanism for proving global convergence in filter-SQP （sequence of quadratic programming） method with the nonlinear complementarity problem （NCP） function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.

利用Fischer-Burmeister函数对非线性互补问题的研究

Facch ine i在研究将变分不等式问题化为一般求极小问题时,给出了一个有界水平集的结果。本文将这个结论推广到非线性互补问题。

Trust Region Algorithm for a Class of Nonlinear Complementarity Problem

In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

A Potential-Reduction Algorithm for Linear Complementarity Problems

Feasible-interior-point algorithms start from a strictly feasible interior point, but infeassible-interior-point algorithms just need to start from an arbitrary positive point, we give a potential reduction algorithm from an infeasible-starting-point for a class of non-monotone linear complementarity problem. Its polynomial complexity is analyzed. After finite iterations the algorithm produces an approximate solution of the problem or shows that there is no feasible optimal solution in a large region. Key words linear complementarity problems - infeasible-starting-point - P-matrix - potential function CLC number O 221 Foundation item: Supported by the National Natural Science Foundation of China (70371032) and the Doctoral Educational Foundation of China of the Ministry of Education (20020486035)Biography: Wang Yan-jin (1976-), male, Ph. D candidate, research direction: optimal theory and method.

Smoothing Newton Algorithm for Solving Generalized Complementarity Problem

The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.

Homotopy Continuation Method for Linear Complementarity Problems

It is well known that a linear complementarity problem (LCP) can be formulated as a system of nonsmooth equations F(x) = 0, where F is a map from Rninto itself. Using the aggregate function, we construct a smooth Newton homotopy H(x,t) = 0. Under certain assumptions, we prove the existence of a smooth path defined by the Newton homotopy which leads to a solution of the original problem, and study limiting properties of the homotopy path.

A Class of Smoothing Modulus-Based Iterative Method for Solving Implicit Complementarity Problems

In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.

Evaluating alternative hypotheses behind biodiversity and multifunctionality relationships in the forests of Northeastern China

Background:The importance of biodiversity in maintaining multiple ecosystem functions has been widely accepted.However,the specific mechanisms affecting biodiversity and ecosystem multifunctionality(BEMF)relationships in forests are largely unknown.This is particularly evident for the macroscale of a large forested landscape.Methods:Based on 412 one-tenth hectare field plots distributed over forested areas across northeastern China,we evaluated three alternative hypotheses explaining the relationships between BEMF,namely:niche complementarity,mass ratio,and vegetation quantity effect.We used Rao's quadratic entropy and community weighted mean trait values to quantify forest“biodiversity”.These two variables represent two complementary aspects of functional properties,which are in line with niche complementary and mass ratio effects,respectively.Results:Ecosystem multifunctionality was negatively associated with the community weighted mean values of acquisitive traits(a proxy of mass ratio effect).Rao's quadratic entropy(a proxy of niche complementarity)had no relationship with ecosystem multifunctionality.Higher stand biomass greatly increased ecosystem multifunctionality,which is in line with the vegetation quantity effect.Our results confirm that in the temperate forests of northeastern China,the relationship of BEMF was primarily affected by vegetation quantity,followed by mass ratio effects.Conclusions:The results of this study contribute to a better understanding of the main drivers of ecosystem multifunctionality in forest ecosystems.The results of this study provide additional evidence to support the vegetation quantity and mass ratio hypotheses in forest ecosystems.

Properties of a family of merit functions and a merit function method for the NCP

A family of merit functions are proposed, which are the generalization of several existing merit functions. A number of favorable properties of the proposed merit functions are established. By using these properties, a merit function method for solving nonlinear complementarity problem is investigated, and the global convergence of the proposed algorithm is proved under some standard assumptions. Some preliminary numerical results are given.

Functional composition of tall-statured trees underpins aboveground biomass in tropical forests

The influences of trait diversity(i.e.,the niche complementarity effect)and functional composition(i.e.,the mass ratio effect)on aboveground biomass(AGB)is a highly debated topic in forest ecology.Therefore,further studies are needed to explore these mechanisms in unstudied forest ecosystems to enhance our understanding,and to provide guidelines for specific forest management.Here,we hypothesized that functional composition would drive AGB better than trait diversity and stem size inequality in the(sub-)tropical forests of Nepal.Using data from 101 forest plots,we tested 25 structural equation models(SEMs)to link elevation,stem DBH inequality,trait diversity(i.e.,trait richness,evenness,dispersion and divergence),functional composition[i.e.,community-weighted of maximum height mean(CWM of Hmax),specific leaf area(CWM of SLA),leaf dry matter content(CWM of LDMC),and wood density(CWM of WD)]and AGB.The best-fitted SEMs indicated that CWM of Hmax promoted AGB while overruling the impacts of trait diversity indices on AGB.However,low trait diversity indices were linked with higher AGB while overruling the effects of CWM of SLA,LDMC and WD on AGB.In addition,AGB decreased with increasing elevation,whereas stem size inequality did not influence AGB.Our results suggest that divergent species’functional strategies could shape AGB along an altitudinal gradient in tropical forests.We argue that forest management practices should include plant functional traits in the management plan for the co-benefits of biodiversity conservation and carbon sequestration that underpins human wellbeing.

Assessing above-ground biomass-functional diversity relationships in temperate forests in northern Mexico

Background:Studies on the relationship between biodiversity and ecosystem productivity have suggested that species richness and functional diversity are the main drivers of ecosystem processes.Several patterns on this relationship have been found,including positive,unimodal,negative,and neutral trends,keeping the issue controversial.In this study,taxonomic diversity and functional diversity as drivers of above-ground biomass(AGB)were compared,and the mechanisms that influence biomass production were investigated by testing the complementarity and the mass-ratio hypotheses.Methods:Using data from 414 permanent sample plots,covering 23%of temperate forest in the Sierra Madre Oriental(México),we estimated the above-gound biomass(AGB),taxonomic and functional diversity indices,as well as community weighted mean values(CWM)for three functional traits(maximum height,leaf size and wood density)for trees≥7.5 cm DBH,in managed and unmanaged stands.To compare taxonomic diversity differences between managed and unmanaged stands we carried out a rarefaction analysis.Furthermore,we evaluated the relationship between AGB and taxonomic and functional diversity metrics,as well as CWM traits throught spatial autoregressive models.Results:We found a hump-shaped relationship between AGB and species richness in managed and unmanaged forests.CMW of maximum height was the most important predictor of AGB in both stands,which suggested that the mechanism underlaying the AGB-diversity relationship is the dominance of some highly productive species,supporting the mass-ratio hypothesis.Above-ground biomass was significantly correlated with three of the five functional diversity metrics,CWM maximum height and species richness.Our results show the importance of taking into account spatial autocorrelation in the construction of predictive models to avoid spurious patterns in the AGBdiversity relationship.Conclusion:Species richness,maximum height,functional richness,functional dispersion and RaoQ indices relate with above-ground biomass production in temperate mixed-species and uneven-aged forests of northern Mexico.These forests show a hump-shaped AGB-species richness relationship.Functional diversity explains better AGB production than classical taxonomic diversity.Community weighted mean traits provide key information to explain stand biomass in these forests,where maximum tree height seems to be a more suitable trait for understanding the biomass accumulation process in these ecosystems.Although the impact of forest management on biodiversity is still debated,it has not changed the AGB-diversity relationships in the forests of the Sierra Madre Occidental,Mexico.

Spectral Gradient Algorithm Based on the Generalized Fiser-Burmeister Function for Sparse Solutions of LCPS

This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization model is proposed for relaxation. We establish the equivalent unconstrained minimization reformation of the NCP-function. Based on the generalized Fiser-Burmeister function, a sequential smoothing spectral gradient method is proposed to solve the equivalent problem. Numerical results are given to show the efficiency of the proposed method.

Solving frictional contact problems by two aggregate-function-based algorithms

Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.