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  1. Convex optimization

    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 polynomial-time algorithms, whereas mathematical optimization is in general NP-hard. Wikipedia

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  2. en.wikipedia.org

    Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, [1] whereas mathematical optimization is in general NP-hard.
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  4. This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimization, strongly influenced by Nesterov's seminal book and Nemirovski's lecture ...
    Author:Sébastien BubeckPublished:2014
  5. web.stanford.edu

    applications of convex optimization are still waiting to be discovered. There are great advantages to recognizing or formulating a problem as a convex optimization problem. The most basic advantage is that the problem can then be solved, very reliably and efficiently, using interior-point methods or other special methods for convex optimization.
  6. This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications, presenting the basic theory, and concentrating on modeling aspects and results that are useful in applications. Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite ...
  7. Figure 4 illustrates convex and strictly convex functions. Now consider the following optimization problem, where the feasible re-gion is simply described as the set F: P: minimize x f (x) s.t. x ∈F Proposition 5.3 Suppose that F is a convex set, f: F→ is a convex function, and x¯ is a local minimum of P . Then ¯x is a global minimum of f ...
  8. Convex optimization problems 4-16 . Linear program (LP) minimize cTx + d subject to Gx h Ax = b • convex problem with affine objective and constraint functions • feasible set is a polyhedron P x ⋆ −c Convex optimization problems 4-17 . Examples
  9. people.eecs.berkeley.edu

    Convex Optimization Problems Convex Optimization Problems Definition An optimization problem is convex if its objective is a convex function, the inequality constraints fj are convex, and the equality constraints hj are affine minimize x f0(x) (Convex function) s.t. fi(x) ≤ 0 (Convex sets) hj(x) = 0 (Affine)
  10. cs229.stanford.edu

    by Stephen Boyd. If you are interested in pursuing convex optimization further, these are both excellent resources. 2 Convex Sets We begin our look at convex optimization with the notion of a convex set. Definition 2.1 A set C is convex if, for any x,y ∈ C and θ ∈ R with 0 ≤ θ ≤ 1, θx+(1−θ)y ∈ C.
  11. This course concentrates on recognizing and solving convex optimization problems that arise in applications. The syllabus includes: convex sets, functions, and optimization problems; basics of convex analysis; least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems; optimality conditions, duality theory, theorems of alternative, and ...
  12. cse.iitb.ac.in

    Convex optimization problem solving convex optimization problems no analytical solution reliable and efficient algorithms computation time (roughly) proportional to {n3, n2m, F}, where F is cost of evaluating fi's and their first and second derivative almost a technology using convex optimization often difficult to recognize

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