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User's Guide For YALL1: Your Algorithms for L1 Optimization
This User's Guide describes the functionality and basic usage of the Matlab package YALL1 for L1 minimization. The one-for-six algorithm used in the YALL1 solver is briefly introduced in the appendix.
Maximum Stable Set Formulations and Heuristics Based on Continuous Optimization
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 ...
Interior-Point Gradient Methods with Diagonal-Scalings for Simple-Bound Constrained Optimization
In this paper, we study diagonally scaled gradient methods for simple-bound constrained optimization in a framework almost identical to that for unconstrained optimization, except that iterates are kept within the interior ...
An Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems
We study an interior-point gradient method for solving a class of so-called totally nonnegative least squares problems. At each iteration, the method decreases the residual norm along a diagonally scaled negative gradient ...
A Geometric Approach to Fluence Map Optimization in IMRT Cancer Treatment Planning
Intensity-modulated radiation therapy (IMRT) is a state-of-the-art technique for administering radiation to cancer patients. The goal of a treatment is to deliver a prescribed amount of radiation to the tumor, while limiting ...
A General Robust-Optimization Formulation for Nonlinear Programming
Most research in robust optimization has so far been focused on inequality-only, convex conic programming with simple linear models for uncertain parameters. Many practical optimization problems, however, are nonlinear and ...
On the Equivalence Between a Commonly Used Correlation Coefficient and a Least Squares Function
Many objective functions have been proposed in X-ray crystallography to solve the molecular replacement (MR) problem and other optimization problems. In this paper, we establish the equivalence between optimizing two target ...
Case Studies For a First-Order Fobust Nonlinear Programming
In this paper, we conduct three case studies to assess the effectiveness of a recently proposed first-order method for robust nonlinear programming (Ref. 1). Three robust nonlinear programming problems were chosen from the ...
Variationally Constrained Numerical Solution of Electrical Impedance Tomography
We propose a novel, variational inversion methodology for the electrical impedance tomography problem, where we seek electrical conductivity σ inside a bounded, simply connected domain Ω, given simultaneous measurements ...
Computational Experience with Lenstra's Algorithm
Integer programming is an important mathematical approach for many decision-making problems. In this field, a major theoretical breakthrough came in 1983 when H. W. Lenstra, Jr. proposed a polynomial-time algorithm for a ...