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First order optimization methods often perform poorly on ill-conditioned optimization problems. However, by preconditioning the problem data and solving the preconditioned problem, the performance of ...
On the Convergence of a Multi-Agent Projected Stochastic Gradient Algorithm
Multi-Agent Projected Stochastic Gradient Algorithm Optimization and Control
2011/9/5
Abstract: We introduce a new framework for the convergence analysis of a class of distributed constrained non-convex optimization algorithms in multi-agent systems. The aim is to search for local mini...
Conditional Gradient Algorithms for Rank-One Matrix Approximations with a Sparsity Constraint
Sparse Principal Component Analysis PCA Conditional Gradient Algorithms Sparse Eigenvalue Problems
2011/8/26
Abstract: The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine le...
Optimal estimates for the gradient of harmonic functions in the unit disk
Harmonic functions Bloch functions Hardy spaces.
2011/2/21
Concrete sharp constants in a pointwise estimate of the gradient of a harmonic function in the unit disk are obtained under the assumption that function belong to Hardy space hp, p > 1. This gen-erali...
Lecture Notes on Gradient Flows and Optimal Transport
Lecture Notes Gradient Flows Optimal Transport
2010/12/9
We present a short overview on the strongest variational formulation for gradient flows of geodesically -convex functionals in metric spaces, with applications to diffusion equations in Wasserstein s...