Results 1  10
of
134,096
A survey of the Slemma
 SIAM Review
"... Abstract. In this survey we review the many faces of the Slemma, a result about the correctness of the Sprocedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry, and linear algebra as ..."
Abstract

Cited by 59 (1 self)
 Add to MetaCart
with various areas of mathematics. We prove some new duality results and present applications from control theory, error estimation, and computational geometry. Key words. Slemma, Sprocedure, control theory, nonconvex theorem of alternatives, numerical range, relaxation theory, semidefinite optimization
The generalized trust region subproblem
, 2012
"... The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, ℓ ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, ℓ ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function
The generalized trust region subproblem
, 2012
"... The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, ℓ ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function. ..."
Abstract
 Add to MetaCart
The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, ℓ ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
Abstract

Cited by 557 (9 self)
 Add to MetaCart
An algorithm for solving large nonlinear optimization problems with simple bounds is described.
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
Abstract

Cited by 543 (11 self)
 Add to MetaCart
The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
Abstract

Cited by 800 (26 self)
 Add to MetaCart
of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
Abstract

Cited by 557 (12 self)
 Add to MetaCart
We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
The strength of weak learnability
 Machine Learning
, 1990
"... Abstract. This paper addresses the problem of improving the accuracy of an hypothesis output by a learning algorithm in the distributionfree (PAC) learning model. A concept class is learnable (or strongly learnable) if, given access to a Source of examples of the unknown concept, the learner with h ..."
Abstract

Cited by 861 (24 self)
 Add to MetaCart
well. In addition, the construction has some interesting theoretical consequences, including a set of general upper bounds on the complexity of any strong learning algorithm as a function of the allowed error e.
Results 1  10
of
134,096