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===소스=== | ===소스=== | ||
<references /> | <references /> | ||
| + | |||
| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q463359 Q463359] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'convex'}, {'LEMMA': 'optimization'}] | ||
| + | * [{'LOWER': 'convex'}, {'LEMMA': 'optimisation'}] | ||
| + | |||
| + | == 노트 == | ||
| + | |||
| + | ===말뭉치=== | ||
| + | # Convex optimization studies the problem of minimizing a convex function over a convex set.<ref name="ref_8555a9b0">[https://convex-optimization.github.io/ Algorithms for Convex Optimization]</ref> | ||
| + | # Consequently, convex optimization has broadly impacted several disciplines of science and engineering.<ref name="ref_8555a9b0" /> | ||
| + | # In the last few years, algorithms for convex optimization have revolutionized algorithm design, both for discrete and continuous optimization problems.<ref name="ref_8555a9b0" /> | ||
| + | # Surprisingly, algorithms for convex optimization have also been used to design counting problems over discrete objects such as matroids.<ref name="ref_8555a9b0" /> | ||
| + | # This course concentrates on recognizing and solving convex optimization problems that arise in applications.<ref name="ref_478e5b43">[https://www.edx.org/course/convex-optimization Convex Optimization]</ref> | ||
| + | # In a convex optimization problem, the feasible region -- the intersection of convex constraint functions -- is a convex region, as pictured below.<ref name="ref_bce6add8">[https://www.solver.com/convex-optimization Optimization Problem Types - Convex Optimization]</ref> | ||
| + | # A non-convex optimization problem is any problem where the objective or any of the constraints are non-convex, as pictured below.<ref name="ref_bce6add8" /> | ||
| + | # Convex optimization has practical applications for the following.<ref name="ref_a964fd82">[https://en.wikipedia.org/wiki/Convex_optimization#:~:text=Convex%20optimization%20is%20a%20subfield,is%20in%20general%20NP%2Dhard. Convex optimization]</ref> | ||
| + | # Ref CVX MATLAB Interfaces with SeDuMi and SDPT3 solvers; designed to only express convex optimization problems.<ref name="ref_a964fd82" /> | ||
| + | # In this blog post, you will learn about convex optimization concepts and different techniques with the help of examples.<ref name="ref_84d8626c">[https://vitalflux.com/convex-optimization-explained-concepts-examples/ Convex optimization explained: Concepts & Examples]</ref> | ||
| + | # Convex optimization can be used to also optimize an algorithm which will increase the speed at which the algorithm converges to the solution.<ref name="ref_84d8626c" /> | ||
| + | # To solve convex optimization problems, machine learning techniques such as gradient descent are used.<ref name="ref_84d8626c" /> | ||
| + | # Convexity plays an important role in convex optimizations.<ref name="ref_84d8626c" /> | ||
| + | # 113 viii Contents 127 4 Convex optimization problems 4.1 Optimization problems . . . . . . . . . . . . . . . . . . . . . . . . . .<ref name="ref_8e266cba">[https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf Convex optimization]</ref> | ||
| + | # The Wolfram Language provides the major convex optimization classes, their duals and sensitivity to constraint perturbation.<ref name="ref_ffcef3e6">[https://reference.wolfram.com/language/guide/ConvexOptimization.html Convex Optimization—Wolfram Language Documentation]</ref> | ||
| + | # This course focuses on convex optimization theory and algorithms.<ref name="ref_89804192">[http://www.ece.tufts.edu/ee/194CO/ EE194 – Convex Optimization]</ref> | ||
| + | # The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years.<ref name="ref_778240bf">[http://www.athenasc.com/convexduality.html Textbook: Convex Optimization Theory]</ref> | ||
| + | # It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory).<ref name="ref_778240bf" /> | ||
| + | # "The textbook, Convex Optimization Theory (Athena) by Dimitri Bertsekas, provides a concise, well-organized, and rigorous development of convex analysis and convex optimization theory.<ref name="ref_778240bf" /> | ||
| + | # Convex optimization is the process of minimizing a convex objective function subject to convex constraints or, equivalently, maximizing a concave objective function subject to convex constraints.<ref name="ref_14bce021">[https://www.mathworks.com/discovery/convex-optimization.html Convex Optimization]</ref> | ||
| + | # Online convex optimization concerns a sequence of convex functions f (; z1), . . .<ref name="ref_87aadca2">[https://www.cs.cornell.edu/~sridharan/convex.pdf Stochastic convex optimization]</ref> | ||
| + | # The results for the online setting prompt us to ask whether similar results, requiring only Lipschitz continuity, can also be obtained for stochastic convex optimization.<ref name="ref_87aadca2" /> | ||
| + | # This might lead us to think that Lipschitz-continuity is not enough to make stochastic convex optimization possible, even though it is enough to ensure on- line convex optimization is possible.<ref name="ref_87aadca2" /> | ||
| + | # This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms.<ref name="ref_99d990e6">[https://www.microsoft.com/en-us/research/publication/convex-optimization-algorithms-complexity/ Convex Optimization: Algorithms and Complexity]</ref> | ||
| + | # CVXR is an R package that provides an object-oriented modeling language for convex optimization, similar to CVX , CVXPY , YALMIP , and Convex.jl .<ref name="ref_11de7d14">[https://cran.r-project.org/web/packages/CVXR/vignettes/cvxr_intro.html Disciplined Convex Optimization in R]</ref> | ||
| + | # It allows the user to formulate convex optimization problems in a natural mathematical syntax rather than the restrictive standard form required by most solvers.<ref name="ref_11de7d14" /> | ||
| + | # 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.<ref name="ref_11de7d14" /> | ||
| + | # 258 2.4 Conjugate gradient 3 Dimension-free convex optimization 262 3.1 Projected subgradient descent for Lipschitz functions . .<ref name="ref_2899b0a0">[http://sbubeck.com/Bubeck15.pdf Foundations and trends r(cid:13) in machine learning]</ref> | ||
| + | # 289 4 Almost dimension-free convex optimization in non-Euclidean spaces 296 4.1 Mirror maps . . . . . . . . . . . . . . . . . . . . . . . .<ref name="ref_2899b0a0" /> | ||
| + | # Some convex optimization problems in machine learning 233 we proceed to give a few important examples of convex optimization problems in machine learning.<ref name="ref_2899b0a0" /> | ||
| + | # 1.1 Some convex optimization problems in machine learning Many fundamental convex optimization problems in machine learning take the following form: min.<ref name="ref_2899b0a0" /> | ||
| + | ===소스=== | ||
| + | <references /> | ||
| + | |||
| + | == 메타데이터 == | ||
| + | |||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q463359 Q463359] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'convex'}, {'LEMMA': 'optimization'}] | ||
| + | * [{'LOWER': 'convex'}, {'LEMMA': 'optimisation'}] | ||
2022년 7월 6일 (수) 00:56 기준 최신판
노트
- CVXOPT is a free software package for convex optimization based on the Python programming language.[1]
- Convex optimization studies the problem of minimizing a convex function over a convex set.[2]
- Surprisingly, algorithms for convex optimization have also been used to design counting problems over discrete objects such as matroids.[2]
- Simultaneously, algorithms for convex optimization have become central to many modern machine learning applications.[2]
- The goal of this book is to enable a reader to gain an in depth understanding of algorithms for convex optimization.[2]
- Convex optimization has many applications ranging from operations research and machine learning to quantum information theory.[3]
- The goal of this course is to investigate in-depth and to develop expert knowledge in the theory and algorithms for convex optimization.[4]
- The lecture slides are adopted from Dr. Stephen Boyd's letcture notes on Convex Optimization at Standord University.[5]
- x + &bgr; y ) = &agr; f i( x ) + &bgr; f i( y )), the problem is said to be one of convex optimization.[6]
- Note that linear programming is a special case of convex optimization, where the objective and constraint functions are all linear.[6]
- If a problem can be transformed to an equivalent convex optimization, then ability to visualize its geometry is acquired.[7]
- Study of equivalence, sameness, and uniqueness therefore pervade study of convex optimization.[7]
- A MOOC on convex optimization, CVX101, was run from 1/21/14 to 3/14/14.[8]
- Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets.[9]
- Extensions of convex optimization include the optimization of biconvex, pseudo-convex, and quasiconvex functions.[9]
- This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms.[10]
- A wealth of existing methodology for convex optimization can then be used to identify points arbitrarily close to the true global optimum.[11]
소스
- ↑ Home — CVXOPT
- ↑ 2.0 2.1 2.2 2.3 Algorithms for Convex Optimization
- ↑ Pushing the boundaries of convex optimization
- ↑ Industrial Engineering & Management Sciences
- ↑ CSCI 5254: Convex Optimization and Its Applications
- ↑ 6.0 6.1 Convex Optimization
- ↑ 7.0 7.1 Convex Optimization
- ↑ Convex Optimization – Boyd and Vandenberghe
- ↑ 9.0 9.1 Convex optimization
- ↑ Convex Optimization: Algorithms and Complexity
- ↑ Using convex optimization of autocorrelation with constrained support and windowing for improved phase retrieval accuracy
메타데이터
위키데이터
- ID : Q463359
Spacy 패턴 목록
- [{'LOWER': 'convex'}, {'LEMMA': 'optimization'}]
- [{'LOWER': 'convex'}, {'LEMMA': 'optimisation'}]
노트
말뭉치
- Convex optimization studies the problem of minimizing a convex function over a convex set.[1]
- Consequently, convex optimization has broadly impacted several disciplines of science and engineering.[1]
- In the last few years, algorithms for convex optimization have revolutionized algorithm design, both for discrete and continuous optimization problems.[1]
- Surprisingly, algorithms for convex optimization have also been used to design counting problems over discrete objects such as matroids.[1]
- This course concentrates on recognizing and solving convex optimization problems that arise in applications.[2]
- In a convex optimization problem, the feasible region -- the intersection of convex constraint functions -- is a convex region, as pictured below.[3]
- A non-convex optimization problem is any problem where the objective or any of the constraints are non-convex, as pictured below.[3]
- Convex optimization has practical applications for the following.[4]
- Ref CVX MATLAB Interfaces with SeDuMi and SDPT3 solvers; designed to only express convex optimization problems.[4]
- In this blog post, you will learn about convex optimization concepts and different techniques with the help of examples.[5]
- Convex optimization can be used to also optimize an algorithm which will increase the speed at which the algorithm converges to the solution.[5]
- To solve convex optimization problems, machine learning techniques such as gradient descent are used.[5]
- Convexity plays an important role in convex optimizations.[5]
- 113 viii Contents 127 4 Convex optimization problems 4.1 Optimization problems . . . . . . . . . . . . . . . . . . . . . . . . . .[6]
- The Wolfram Language provides the major convex optimization classes, their duals and sensitivity to constraint perturbation.[7]
- This course focuses on convex optimization theory and algorithms.[8]
- The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years.[9]
- It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory).[9]
- "The textbook, Convex Optimization Theory (Athena) by Dimitri Bertsekas, provides a concise, well-organized, and rigorous development of convex analysis and convex optimization theory.[9]
- Convex optimization is the process of minimizing a convex objective function subject to convex constraints or, equivalently, maximizing a concave objective function subject to convex constraints.[10]
- Online convex optimization concerns a sequence of convex functions f (; z1), . . .[11]
- The results for the online setting prompt us to ask whether similar results, requiring only Lipschitz continuity, can also be obtained for stochastic convex optimization.[11]
- This might lead us to think that Lipschitz-continuity is not enough to make stochastic convex optimization possible, even though it is enough to ensure on- line convex optimization is possible.[11]
- This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms.[12]
- CVXR is an R package that provides an object-oriented modeling language for convex optimization, similar to CVX , CVXPY , YALMIP , and Convex.jl .[13]
- It allows the user to formulate convex optimization problems in a natural mathematical syntax rather than the restrictive standard form required by most solvers.[13]
- 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.[13]
- 258 2.4 Conjugate gradient 3 Dimension-free convex optimization 262 3.1 Projected subgradient descent for Lipschitz functions . .[14]
- 289 4 Almost dimension-free convex optimization in non-Euclidean spaces 296 4.1 Mirror maps . . . . . . . . . . . . . . . . . . . . . . . .[14]
- Some convex optimization problems in machine learning 233 we proceed to give a few important examples of convex optimization problems in machine learning.[14]
- 1.1 Some convex optimization problems in machine learning Many fundamental convex optimization problems in machine learning take the following form: min.[14]
소스
- ↑ 1.0 1.1 1.2 1.3 Algorithms for Convex Optimization
- ↑ Convex Optimization
- ↑ 3.0 3.1 Optimization Problem Types - Convex Optimization
- ↑ 4.0 4.1 Convex optimization
- ↑ 5.0 5.1 5.2 5.3 Convex optimization explained: Concepts & Examples
- ↑ Convex optimization
- ↑ Convex Optimization—Wolfram Language Documentation
- ↑ EE194 – Convex Optimization
- ↑ 9.0 9.1 9.2 Textbook: Convex Optimization Theory
- ↑ Convex Optimization
- ↑ 11.0 11.1 11.2 Stochastic convex optimization
- ↑ Convex Optimization: Algorithms and Complexity
- ↑ 13.0 13.1 13.2 Disciplined Convex Optimization in R
- ↑ 14.0 14.1 14.2 14.3 Foundations and trends r(cid:13) in machine learning
메타데이터
위키데이터
- ID : Q463359
Spacy 패턴 목록
- [{'LOWER': 'convex'}, {'LEMMA': 'optimization'}]
- [{'LOWER': 'convex'}, {'LEMMA': 'optimisation'}]