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Title : Convex Optimization Algorithms
ISBN : 1886529280
Release Date : 2015-02-10
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Textbook Convex Optimization Algorithms Convex Optimization Algorithms The latter book focuses on convexity theory and optimization duality while the present book focuses on algorithmic issues The two books share mathematical prerequisites notation and style and together cover the entire finitedimensional convex optimization field Convex optimization Wikipedia Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets Many classes of convex optimization problems admit polynomialtime algorithms 1 whereas mathematical optimization is in general NPhard Textbook Convex Optimization Algorithms The following sets of slides reflect an increasing emphasis on algorithms over time Convex Analysis and Optimization 2014 Lecture Slides for MIT course 6253 Spring 2014 Based on the book Convex Optimization Theory Athena Scientific 2009 and the book Convex Optimization Algorithms Athena Scientific 2014 Convex Optimization Modeling and Algorithms Convex Optimization Modeling and Algorithms Lieven Vandenberghe Electrical Engineering Department UC Los Angeles Tutorial lectures 21st Machine Learning Summer School Kyoto August 2930 2012 ConvexOptimizationAlgorithmsand Complexity we proceed to give a few important examples of convex optimization problemsinmachinelearning 11Someconvexoptimizationproblemsinmachinelearning Manyfundamentalconvexoptimizationproblemsinmachinelearning takethefollowingform min x∈Rn Xm i1 f ix λRx 11 where the functions f 1f mRare convex and λ ≥0 is a fixed Nonlinear Programming 3rd Edition 2016 Convex Optimization Theory 2009 It covers descent algorithms for unconstrained and constrained optimization Lagrange multiplier theory interior point and augmented Lagrangian methods for linear and nonlinear programs duality theory and major aspects of largescale optimization Convex Optimization Stanford University Since any linear program is therefore a convex optimization problem we can consider convex optimization to be a generalization of linear programming 111 Applications The optimization problem 11 is an abstraction of the problem of making the best possible choice of a vector in Rn from a set of candidate choices 14054980 Convex Optimization Algorithms and Complexity Convex Optimization Algorithms and Complexity We provide a gentle introduction to structural optimization with FISTA to optimize a sum of a smooth and a simple nonsmooth term saddlepoint mirror prox Nemirovskis alternative to Nesterovs smoothing and a concise description of interior point methods Introduction to Online Convex Optimization core algorithms for online convex optimization The rest of the book deals with more advanced algorithms more di cult settings and relationships to wellknown machine learning paradigms Contents Preface iii 1 Introduction 3 11 The online convex optimization model 4 Dimitri P Bertsekas Massachusetts Institute of Technology Interest in convex optimization has become intense due to widespread applications in fields such as largescale resource allocation signal processing and machine learning This book aims at an uptodate and accessible development of algorithms for solving convex optimization problems