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.

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.

Empirical Analysis of City Contact in Zhujiang(Pearl) River Delta, China

In traditional urban geography, city contact research is a classic study element in city research. In general, researchers use the traditional gravity model to characterize the contacts that exist between two cities. The traditional gravity model assumes ideal conditions, but these preconditions and their results often do not exist in realistic conditions. Thus, we used a modified gravity model to characterize the city contacts within a specific region. This model considers factors such as intercity complementarities, government intervention, and the diversity of the transportation infrastructure which is characterized as the transportation distance instead of the traditional Euclidean distance. We applied this model to an empirical study of city contact in the Zhujiang(Pearl) River Delta(PRD) of China. The regression results indicated that the modified gravity model could measure city contact more accurately and comprehensively than the traditional gravity model, i.e., it yielded a higher adjusted R2 value(0.379) than the traditional gravity model result(0.259). Our study also suggests that, in addition to urban-regional and metropolitan development, the complementarities of the basic functions of cities at the administrative and market levels, as well as the corporeal and immaterial levels, play very significant roles in the characterization of city contact. Given the complexity of city contact, it will be necessary to consider more relevant influential factors in the modified gravity model to characterize the features of city contact in the future.

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.

A New Complementarity Function and Applications in Stochastic Second-Order Cone Complementarity Problems

This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone.We show that the ERM model has bounded level sets under the stochastic weak R0-property.We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications.Then,we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis.Furthermore,we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks.