The textbook, Convex Optimization Theory (Athena) by Dimitri Bertsekas, provides a concise, well-organized, and rigorous development of convex analysis and. Dimitri Bertsekas; Convex Optimization MOOC from Stanford Online · Convex downloadable book; Convex Optimization Theory - by Dimitri P. Bertsekas. [PDF] Convex Optimization Theory 1st Edition by Dimitri P. Bertsekas in Books, Other Books | site.
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This chapter aims to supplement the book Convex Optimization Theory, results are suitably combined, as discussed by Nedic, Bertsekas, and Borkar. Convex Optimization Theory. by Dimitri P. Bertsekas. ISBN: , Publication: June, , pages, hardcover. Price: $ Athena Scientific, with material on convex optimization algorithms. results are suitably combined, as discussed by Nedic, Bertsekas.
Proposition 4. The feasible solutions of the max crossing problem are restricted by the horizontal directions of recession of M. This is the essence of the following proposition. Section 4. Some Special Cases There are several interesting special cases where the set M is the epigraph of some function. An example of this type is minimization with inequality constraints: minimize f x B.
Nocedal and S. Convex Optimization.
Boyd and L. Cambridge University Press, Cambridge, Kluwer, Convex Optimization: Algorithms and Complexity. Athena Scientific, Belmont, Massachusetts.
Efficient Methods in Convex Programming.
Assignment 3 Deadline: Friday, October 13, 1pm. Five problems 10 points each for Problems 1 through 4, 20 points for Problem 5. All problems are given in the template. Final group project Group size: 1, 2, or 3 students each group.
No more than 3.
Requirements: read one or a few related papers under the same topic submit both a reading report or a set of slides that describe the background, motivation, main methods, numerical results, and future direction The submitted documents will be read by the instructor.
Points will be taken for missing major parts, missing major novelties or contributions, missing major references, or any significant mathematical errors.
Deadlines: Group formation: Nov Email the instructor by email and copy all group mates. Topic selection: Nov 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.
Detailed solutions of all the exercises are internet-posted in the book's www page. Another common stylistic element of the two books is the close link between the theoretical treatment of convexity and its application to optimization.
For example, simultaneously with the development of some of 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 applications to duality and saddle point theory; in Chapter 4, after the discussion of polyhedral convexity, we discuss its application in linear, integer, and convex programming; and in Chapter 6, after the discussion of subgradients, we discuss their use in optimality conditions and minimization algorithms.
We follow this style in the remaining chapters, although having developed in Chapters most of the needed convexity theory, the discussion in Chapters is more heavily weighted towards optimization.
Some of the novel expository features of the book have been maintained in the present version as well. In particular, minimax theory and constrained optimization duality have been developed in a unified way, as special cases of the duality between two simple but fundamental geometrical problems: In several contexts, including duality, it provides a powerful and insightful analytical machinery, which is far more convenient than conjugate function theory.
Another feature shared with the book is the unified approach for developing conditions for existence of solutions of convex optimization problems, conditions for the minimax equality to hold, and conditions for the absence of a duality gap in constrained optimization.
This unification is traced to a simple and fundamental issue: 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. The principle followed here is that "non-starred" sections do not make use of material in "starred" sections.
An instructor who wishes to teach a course from the book has a choice between a few different plans:.
Bertsekas From Wikimization.