Affine-invariant contracting-point methods for Convex Optimization

Augmented Lagrangian Methods and Proximal Point Methods for Convex Optimization

We present a review of the classical proximal point method for nding zeroes of maximal monotone operators, and its application to augmented Lagrangian methods, including a rather complete convergence analysis. Next we discuss the generalized proximal point methods, either with Bregman distances or -divergences, which in turn give raise to a family of generalized augmented Lagrangians, as smooth...

A Mathematical View of Interior Point Methods for Convex Optimization

An Affine Invariant Interest Point Detector

This paper presents a novel approach for detecting affine invariant interest points. Our method can deal with significant affine transformations including large scale changes. Such transformations introduce significant changes in the point location as well as in the scale and the shape of the neighbourhood of an interest point. Our approach allows to solve for these problems simultaneously. It ...

Ma 796s: Convex Optimization and Interior Point Methods

where b, y ∈ IR; ci, xi, si ∈ IRi , Ai ∈ IRm×ni , i = 1, . . . , r. For each i = 1, . . . , r, xi and si are the primal and dual slack variables associated with the ith cone and K∗ i = { si ∈ IRi : xi si ≥ 0, ∀xi ∈ Ki } (3) is the dual cone to Ki. We assume that Ki,K i , i = 1, . . . , r are pointed closed convex cones with nonempty interiors. Let K = K1 × K2 × . . . × Kr be the overall cone in...

Affine Differential Invariants for Invariant Feature Point Detection

Image feature points are detected as pixels which locally maximize a detector function, two commonly used examples of which are the (Euclidean) image gradient and the Harris-Stephens corner detector. A major limitation of these feature detectors are that they are only Euclidean-invariant. In this work we demonstrate the application of a 2D affine-invariant image feature point detector based on ...