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An introduction to optimization
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This review discusses mathematics, linear programming, and set--Constrained and Unconstrained Optimization, as well as methods of Proof and Some Notation, and problems with Equality Constraints.Abstract:
Preface. MATHEMATICAL REVIEW. Methods of Proof and Some Notation. Vector Spaces and Matrices. Transformations. Concepts from Geometry. Elements of Calculus. UNCONSTRAINED OPTIMIZATION. Basics of Set--Constrained and Unconstrained Optimization. One--Dimensional Search Methods. Gradient Methods. Newton's Method. Conjugate Direction Methods. Quasi--Newton Methods. Solving Ax = b. Unconstrained Optimization and Neural Networks. Genetic Algorithms. LINEAR PROGRAMMING. Introduction to Linear Programming. Simplex Method. Duality. Non--Simplex Methods. NONLINEAR CONSTRAINED OPTIMIZATION. Problems with Equality Constraints. Problems with Inequality Constraints. Convex Optimization Problems. Algorithms for Constrained Optimization. References. Index.read more
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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Amir Beck,Marc Teboulle +1 more
TL;DR: A new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically.
Book
Proximal Algorithms
Neal Parikh,Stephen Boyd +1 more
TL;DR: The many different interpretations of proximal operators and algorithms are discussed, their connections to many other topics in optimization and applied mathematics are described, some popular algorithms are surveyed, and a large number of examples of proxiesimal operators that commonly arise in practice are provided.
Journal ArticleDOI
Smooth minimization of non-smooth functions
TL;DR: A new approach for constructing efficient schemes for non-smooth convex optimization is proposed, based on a special smoothing technique, which can be applied to functions with explicit max-structure, and can be considered as an alternative to black-box minimization.
Journal ArticleDOI
An Interior-Point Method for Large-Scale $\ell_1$ -Regularized Least Squares
TL;DR: In this paper, the preconditioned conjugate gradients (PCG) algorithm is used to compute the search direction for sparse least-squares programs (LSPs), which can be reformulated as convex quadratic programs, and then solved by several standard methods such as interior-point methods.
Journal ArticleDOI
Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
Amir Beck,Marc Teboulle +1 more
TL;DR: A fast algorithm is derived for the constrained TV-based image deblurring problem with box constraints by combining an acceleration of the well known dual approach to the denoising problem with a novel monotone version of a fast iterative shrinkage/thresholding algorithm (FISTA).