This file of notes serves as a reference for Zeyuan himself about the materials to be delivered in class. It copies a lot of materials from Prof Michel X. Goemans’ lecture notes on 6.854 in 1994, (see http: //www-math.mit.edu/~goemans/notes-lp.ps), and Prof Sven O. Krumke’s report on interior point methods (see http://optimierung.mathematik.uni-kl.de/~krumke/Notes/interior-lecture. pdf). Ye’s i...

The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ theoremwas generalized byAoki 3 for additive mappings and by Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Rassias 4 has pr...

We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semideenite matrices. We show that the approach is very eecient for graph bisection problems, such as max-cut. Other applications include max-min eigenvalue problems and relaxations for the stable set problem.

A large number of multiscale finite-volume methods have been developed over the past decade to compute conservative approximations to multiphase flow problems in heterogeneous porous media. In particular, several iterative and algebraic multiscale frameworks that seek to reduce the fine-scale residual towards machine precision have been presented. Common for all such methods is that they rely o...

A generalized proximal point method for solving variational inequalities with maximal monotone operators is developed. It admits a successive approximation of the feasible set and of a symmetric component of the operator as well as an inexact solving of the regularized problems. The conditions on the approximation are coordinated with the properties of finite element methods for solving problem...

Detecting dominant points is an important step for shape representation. Most of dominant point detection methods attend to preset or find the region of support of each point. In this paper, we demonstrate an improved method for determining the region of support in the dominant point detection. Instead of setting the regions of support for points independently, the region of support dynamically...

We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as max-cut. Other applications include max-min eigenvalue problems and relaxations for the stable set problem.

The coefficient of consolidation in the Terzaghi theory of consolidation has been commonly determined by fitting the theory to observed compression with time in an incremental loading oedometer test. The Terzaghi theory is applicable to compression and swelling. A similar coefficient governed by horizontal permeability is used in the Barron formulation of consolidation with vertical drains. The...

Xiao Liu, Congying Han, Tiande Guo School of Mathematical Science, University of Chinese Academy of Sciences, Beijing, 100049 Abstract Point sets matching method is very important in computer vision, feature extraction, fingerprint matching, motion estimation and so on. This paper proposes a robust point sets matching method. We present an iterative algorithm that is robust to noise case. First...