"Convex Optimization"의 두 판 사이의 차이

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* ID :  [https://www.wikidata.org/wiki/Q58633368 Q58633368]

2020년 12월 26일 (토) 05:08 판

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  1. A MOOC on convex optimization, CVX101, was run from 1/21/14 to 3/14/14.[1]
  2. This course concentrates on recognizing and solving convex optimization problems that arise in applications.[2]
  3. Because of their desirable properties, convex optimization problems can be solved with a variety of methods.[3]
  4. In layman's terms, the mathematical science of Convex Optimization is the study of how to make a good choice when confronted with conflicting requirements.[4]
  5. If a problem can be transformed to an equivalent convex optimization, then ability to visualize its geometry is acquired.[4]
  6. Study of equivalence, sameness, and uniqueness therefore pervade study of convex optimization.[4]
  7. It also includes many important problems as special case, such as OCO with long term constraints, stochastic constrained convex optimization, and deterministic constrained convex optimization.[5]
  8. The Wolfram Language provides the major convex optimization classes, their duals and sensitivity to constraint perturbation.[6]
  9. Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets.[7]
  10. Extensions of convex optimization include the optimization of biconvex, pseudo-convex, and quasiconvex functions.[7]
  11. Our implementation significantly lowers the barrier to using convex optimization problems in differentiable programs.[8]
  12. The lecture slides are adopted from Dr. Stephen Boyd's letcture notes on Convex Optimization at Standord University.[9]
  13. The basis pursuit minimization of (12.83) is a convex optimization problem that can be reformulated as a linear programming problem.[10]
  14. We first present our main theoretical results on how to train the program state of programmable quantum processors, either via convex optimization or first-order gradient-based algorithms.[11]
  15. When dealing with convex optimization with respect to positive operators, the standard approach is to map the problem to a form that is solvable via SDP (refs.[11]
  16. We employ our convex optimization procedures to find the optimal program state.[11]
  17. Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming.[12]
  18. In this lecture, we develop the basic mathematical preliminaries and tools to study convex optimization.[13]
  19. In this lecture, we introduce a class of cutting plane methods for convex optimization and present an analysis of a special case of it: the ellipsoid method.[13]
  20. CVXPY is a Python-embedded modeling language for convex optimization problems.[14]
  21. The course primarily focuses on techniques for formulating decision problems as convex optimization models that can be solved with existing software tools.[15]
  22. Convex optimization has many applications ranging from operations research and machine learning to quantum information theory.[16]
  23. Convex optimization problems, which involve the minimization of a convex function over a convex set, can be approximated in theory to any fixed precision in polynomial time.[16]
  24. The goal of this course is to investigate in-depth and to develop expert knowledge in the theory and algorithms for convex optimization.[17]
  25. CVXR is an R package that provides an object-oriented modeling language for convex optimization, similar to CVX , CVXPY , YALMIP , and Convex.jl .[18]
  26. It allows the user to formulate convex optimization problems in a natural mathematical syntax rather than the restrictive standard form required by most solvers.[18]
  27. The user is free to construct statistical estimators that are solutions to a convex optimization problem where there may not be a closed form solution or even an implementation.[18]
  28. We develop a sequential convex optimization algorithm to solve the resulting nonsmooth nonconvex optimization problem.[19]
  29. In this paper, we propose the first computationally efficient projection-free algorithm for bandit convex optimization (BCO) with a general convex constraint.[20]
  30. {In this paper, we propose the first computationally efficient projection-free algorithm for bandit convex optimization (BCO) with a general convex constraint.[20]
  31. Convex optimization studies the problem of minimizing a convex function over a convex set.[21]
  32. In the last few years, algorithms for convex optimization have revolutionized algorithm design, both for discrete and continuous optimization problems.[21]
  33. Surprisingly, algorithms for convex optimization have also been used to design counting problems over discrete objects such as matroids.[21]
  34. Simultaneously, algorithms for convex optimization have become central to many modern machine learning applications.[21]
  35. In this paper we lay the foundation of robust convex optimization.[22]
  36. U. This is consistent with a related phenomenon that has been studied in optimization—local strong convexity near the global optimum can improve the convergence rate of convex optimization (43).[23]
  37. x + &bgr; y ) = &agr; f i( x ) + &bgr; f i( y )), the problem is said to be one of convex optimization.[24]
  38. Note that linear programming is a special case of convex optimization, where the objective and constraint functions are all linear.[24]
  39. The next part, chapters 6 through 8, presents a treatment of applications of convex optimization in solving certain problems, arising in engineering, statistics, and mathematics.[24]

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