随笔分类 -  凸优化与非凸优化（Convex and nonconvex optimization)

介绍凸优化与非凸优化的基本概念，常用算法，主要的研究成果及其在机器视觉，压缩感知，深度学习和信息论中的应用。
Big picture of mathematical optimization
摘要：Basic concepts, optimality conditions, different types of optimization, algorithm design techniques 阅读全文
posted @ 2020-06-29 20:47 科研民工 阅读(135) 评论(0) 推荐(0)
Optimality conditions in convex optimization
摘要：first order necessary optimality condition, second order necessary optimality condition, second order sufficient optimality conditions 阅读全文
posted @ 2020-06-29 20:44 科研民工 阅读(157) 评论(0) 推荐(0)
Nonconvex optimization
摘要：\mathbb{R} 阅读全文
posted @ 2020-06-29 09:38 科研民工 阅读(169) 评论(0) 推荐(0)
Convexity or concavity of commonly used functions
摘要：linear function, quadratic function, logarithm function, determinant function, 阅读全文
posted @ 2020-06-29 09:36 科研民工 阅读(128) 评论(0) 推荐(0)
Dual function of commonly used functions
摘要：constant function, linear function, quadratic function, logarithm function, dual function, determinant function, eigenvalue function, sine function, c 阅读全文
posted @ 2020-06-29 09:34 科研民工 阅读(106) 评论(0) 推荐(0)
Proximator of commonly used functions
摘要：indicator function, linear function, quadratic function, norm function, log function, exponential function, the composite of multiple functions, suppo 阅读全文
posted @ 2020-06-29 09:31 科研民工 阅读(116) 评论(0) 推荐(0)
Projection onto commonly used set
摘要：ball, hyperplane, affine set, simplex, second order cone, cubic, intersection of multiple sets,, 阅读全文
posted @ 2020-06-29 09:30 科研民工 阅读(106) 评论(0) 推荐(0)
Commonly used convergence analysis techniques
摘要：convergence types, convergence characterization, convergence analysis techniques, convergence speed 阅读全文
posted @ 2020-06-29 09:28 科研民工 阅读(94) 评论(0) 推荐(0)
Commonly used properties
摘要：convexity, Lipschitz continuity, positive semidefinite,,,, 阅读全文
posted @ 2020-06-29 09:27 科研民工 阅读(69) 评论(0) 推荐(0)
Commonly used algorithms
摘要：gradient descent, Newton's method, trust region, proximal algorithm, admm, interior point method 阅读全文
posted @ 2020-06-29 09:25 科研民工 阅读(100) 评论(0) 推荐(0)
Commonly used algorithm design techniques
摘要：alternating minimization, interior point, line search, trust region, optimality conditions inspired 阅读全文
posted @ 2020-06-29 09:24 科研民工 阅读(120) 评论(0) 推荐(0)
Commonly used objects in convex optimization
摘要：Convex set, conjugate functions, proximator, support function, cone, convex cone, convex hull, second order cone, balls, hyperplanes, affine set, 阅读全文
posted @ 2020-06-29 09:23 科研民工 阅读(129) 评论(0) 推荐(0)