Convergence of a non-interior continuation algorithm for the monotone SCCP

It is well known that the symmetric cone complementarity problem（SCCP） is a broad class of optimization problems which contains many optimization problems as special cases.Based on a general smoothing function,we propose in this paper a non-interior continuation algorithm for solving the monotone SCCP.The proposed algorithm solves at most one system of linear equations at each iteration.By using the theory of Euclidean Jordan algebras,we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions.     

Exact penalty results for mathematical programs with vanishing constraints

A mathematical program with vanishing constraints (MPVC) is a constrained optimization problem arising in certain engineering applications. The feasible set has a complicated structure so that the most familiar constraint qualifications are usually violated. This, in turn, implies that standard penalty functions are typically non-exact for MPVCs. We therefore develop a new MPVC-tailored penalty function which is shown to be exact under reasonable assumptions. This new penalty function can then be used to derive (or recover) suitable optimality conditions for MPVCs.     

Schur-Ostrowski type theorems revisited

In this paper we extend Schur-Ostrowski theorem on Schur-convex functions from majorized vectors to separable ones. For this, we introduce a generalized Schur-Ostrowski?s condition. We apply the obtained result for cone orderings and group-induced cone orderings. Finally, we give some interpretations for absolutely weak majorization and for group majorization on the space of complex matrices.     

On the reduction of elementary bitisors of local cones-an aggregation-type approach

Using a number theoretic approach a method of reducing the elementary divisors of a local cone is presented. This will be done by generating a finite series of integer local optimization problems. The final problem is equivalent to an unidimensional group knapsack problem. It is an aggregation-type approach where the usual condition of identical solutions is replaced by the demand for equal values of objective functions.     

GUS-property for Lorentz cone linear complementarity problems on Hilbert spaces

Given a real(finite-dimensional or infinite-dimensional) Hilbert space H with a Jordan product,we consider the Lorentz cone linear complementarity problem,denoted by LCP(T,Ω,q),where T is a continuous linear operator on H,ΩH is a Lorentz cone,and q ∈ H.We investigate some conditions for which the problem concerned has a unique solution for all q ∈ H(i.e.,T has the GUS-property).Several sufficient conditions and several necessary conditions are given.In particular,we provide two suficient and necessary cond...     

Intersection cuts for convex mixed integer programs from translated cones

We develop a general framework for linear intersection cuts for convex integer programs with full-dimensional feasible regions by studying integer points of their translated tangent cones, generalizing the idea of Balas (1971). For proper (i.e, full-dimensional, closed, convex, pointed) translated cones with fractional vertices, we show that under certain mild conditions all intersection cuts are indeed valid for the integer hull, and a large class of valid inequalities for the integer hull are intersection cuts, computable via polyhedral approximations. We also give necessary conditions for a class of valid inequalities to be tangent halfspaces of the integer hull of proper translated cones. We also show that valid inequalities for non-pointed regular translated cones can be derived as intersection cuts for associated proper translated cones under some mild assumptions.     

A greedy algorithm for yield surface approximation

This Note presents an approximation method for convex yield surfaces in the framework of yield design theory. The proposed algorithm constructs an approximation using a convex hull of ellipsoids such that the approximate criterion can be formulated in terms of second-order conic constraints. The algorithm can treat bounded as well as unbounded yield surfaces. Its efficiency is illustrated on two yield surfaces obtained using up-scaling procedures.     

An Exactly Solvable One-Dimensional Electron-Phonon System

An extended Tomonaga-Luttinger model including for-ward scattering both from electron-electron and electron-pho-non interaction is solved exactly using bosonization techniques. We calculate correlation functions for the relevant instabilities and give a phase diagram.     

一类新的二阶组合切导数及其应用

引进了一种新的切锥,讨论它与相依切锥的关系.借助这种新的切锥引进了一类新的二阶组合切导数,并讨论了它与其他二阶切导数的关系.利用这类新的二阶组合切导数,建立了集值优化分别取得Henig有效元和全局有效元的最优性必要条件.