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Now showing items 1-10 of 67

#### A New Alternating Minimization Algorithm for Total Variation Image Reconstruction

(2007-06)

We propose, analyze and test an alternating minimization algorithm for recovering images from blurry and noisy observa- tions with total variation (TV) regularization. This algorithm arises from a new half-quadratic model ...

#### On the Quadratic Convergence of the Singular Newton's Method

(1992-12)

The purpose of this essay is to describe a situation that we have found particularly exciting in our recent work in interior-point methods for linear programming. To our surprise, we have seen considerable theory developed ...

#### On Numerical Solution of the Maximum Volume Ellipsoid Problem

(2001-08)

In this paper we study practical solution methods for finding the maximum-volume ellipsoid inscribing a given full-dimensional polytope in R n defined by a finite set of affine inequalities. Our goal is to design a ...

#### Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation

(1999-12)

Recently, the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n × n matrix function of a certain form into the positivity constraint on n scalar variables ...

#### A Simple Proof for Recoverability of L1-Minimization (II): the Nonnegativity Case

(2005-09)

When using L1 minimization to recover a sparse, nonnegative solution to a under-determined linear system of equations, what is the highest sparsity level at which recovery can still be guaranteed? Recently, Donoho and ...

#### A Fast Newton's Algorithm for Entropy Maximization in Phase Determination

(1999-05)

A long-standing problem in X-ray crystallography, known as the phase problem, is to determine the phases for a large set of complex variables, called the structure factors of the crystal, given their magnitudes obtained ...

#### Computing a Celis-Dennis Tapia Trust Region Step for Equality Constrained Optimization

(1988-12)

We study an approach for minimizing a convex quadratic function subject to two quadratic constraints. This problem stems from computing a trust region step for an SQP algorithm proposed by Celis, Dennis and Tapia (1984) ...

#### A Fixed-Point Continuation Method for L_1-Regularization with Application to Compressed Sensing

(2007-05)

We consider solving minimization problems with L_1-regularization: min ||x||_1 + mu f(x) particularly for f(x) = (1/2)||Ax-b||M2, where A is m by n and m < n. Our goal is to construct efficient and robust algorithms for ...

#### On Convergence of Minimization Methods: Attraction, Repulsion and Selection

(1999-03)

In this paper, we introduce a rather straightforward but fundamental observation concerning the convergence of the general iteration process. x^(k+1) = x^k - alpha(x^k) [B(x^k)]^(-1) gradf(x^k) for minimizing a function ...

#### Maximum Stable Set Formulations and Heuristics Based on Continuous Optimization

(2000-12)

The stability number for a given graph G is the size of a maximum stable set in G. The Lovasz theta number provides an upper bound on the stability number and can be computed as the optimal value of the Lovasz semidefinite ...