In particular, both books place primary emphasis on theory, rather than algorithms and applications. I also taught for three year… In several contexts, including duality, it provides a powerful and insightful analytical machinery, which is far more convenient than conjugate function theory. at Stanford University (1971-1974) and the Electrical Engineering Dept. of the University of Illinois, Urbana (1974-1979).To provide an alternative, more accessible path to convexity, the most advanced sections have been marked with a star, and can be skipped at first reading. Based on the book "Convex Optimization Theory," Athena Scientific, 2009, and the book "Convex Optimization Algorithms," Athena Scientific, 2014. The latter book focuses on convexity theory and optimization duality, while the 2015 Convex Optimization Algorithms book focuses on algorithmic issues. The min common/max crossing framework is also useful in the analysis and interpretation of conjugate functions, theorems of the alternative, and subdifferential theory. Also, both books use geometric visualization as a principal tool for exposition, and also use end-of-chapter exercises to extend the range of exposition with substantial theoretical and algorithmic results. Most algorithms for minimizing convex over a convex set make use of at least one of the following techniques:. The following sets of slides reflect an increasing emphasis on algorithms over time.includes optimal algorithms based on extrapolation techniques, and associated rate of convergence analysisdevelops comprehensively the theory of descent and approximation methods, including gradient and subgradient projection methods, cutting plane and simplicial decomposition methods, and proximal methodsdescribes and analyzes augmented Lagrangian methods, and alternating direction methods of multiplierscomprehensively covers incremental gradient, subgradient, proximal, and constraint projection methodscontains many examples, illustrations, and exercises Convex Analysis and Optimization, 2014 Lecture Slides for MIT course 6.253, Spring 2014.
For example, simultaneously with the development of someof the basic facts about convexity in Chapters 1 and 2, we discuss elementary optimality conditions, and the question of existence of optimal solutions; in Chapter 3, after presenting the theory of hyperplane separation, we develop some of its applicationsto duality and saddle point theory; in Chapter 4, after the discussion of polyhedralconvexity, we discuss its application in linear, integer, and convex programming; and in Chapter 6,after the discussion of subgradients, we discuss their use in optimalityconditions and minimization algorithms.
The approximation should improve at each step . Hardcover, 9781886529281, 1886529280
The min common/max crossing framework is essentially a geometric version of convex conjugate function theory, but is simpler and unencumbered by functional descriptions. Another common stylistic element of the two books is the close linkbetween the theoretical treatment of convexity and its applicationto optimization. Click here for the lowest price!
This unification is traced to a simple and fundamental issue: the question whether a nested family of closed sets has a nonempty intersection.He consults regularly with private industry and has held editorial positions in several journals.Dr. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. Introduction to Probability, 2nd Edition, by Dimitri P. Bertsekas and John N. Tsitsiklis, 2008, ISBN 978-1-886529-23-6,544 pages 3. I was born in Greece and lived my childhood there. Dynamic Programming and Optimal Control, Two-Volume Set, Convex Optimization Algorithms. In particular, minimax theory and constrained optimization duality have been developed in a unified way, asspecial cases of the duality between two simple but fundamental geometrical problems: the min commonpoint problem and the max crossing point problem. Slides for Prof. Bertsekas' Convex Analysis class at MIT, 2003 We follow this style in the remaining chapters,although having developed in Chapters 1-6 most of the needed convexity theory,the discussion in Chapters 7-8 is more heavily weighted towardsoptimization.An instructor who wishes to teach a course from the book has a choice between a few different plans:Another feature shared with the 2003 book is the unified approach for developing conditions for existence of solutions of convexoptimization problems, conditions for the minimax equality to hold, and conditions for theabsence of a duality gap in constrained optimization.
Slides for Prof. Bertsekas' Convex Analysis class at MIT, 2003 Based on the book "Convex Optimization Theory," Athena Scientific, 2009, and the book "Convex Optimization Algorithms," Athena Scientific, 2014.