Acknowledgement: I would like to thank Prof. Lieven Vandenberghe (UCLA) and Prof. Wotao Yin (UCLA). Most of the slides are motivated or even taken directly from their courses.

第1周，9月22日，课程简介，凸优化问题介绍 lecture notes on introduction, lecture notes on convex sets, demo: sparse_l1_example.m

第2周，9月29日，凸集的定义和判别 Prof. Lieven Vandenberghe's lecture notes on convex sets read chapter 2 in the book “Convex optimization”.

第2周，10月1日，国庆节放假

第3周，10月6日，国庆节放假

第4周，10月13日，凸函数的定义和判别 Prof. Lieven Vandenberghe's lecture notes on convex functions read chapter 3 in the book “Convex optimization”.

第4周，10月15日，数值代数基础，向量，矩阵，范数，子空间，Cholesky分解，QR分解，特征值分解，奇异值分解 Prof. Lieven Vandenberghe's lecture notes on numerical algebra background numerical algebraic background 请读非线性规划参考材料 demo: demo_linalg.m Demo: Sparse matrix-dense vector products using intel MKL BLAS (Basic Linear Algebra Subprograms) LAPACK (Linear Algebra PACKage) Intel Math Kernel Library – Documentation Call LAPACK and BLAS Functions in Matlab

第5周，10月20日，典型的凸优化问题： lecture notes read chapter 4 in in the book “Convex optimization”

第6周，10月27日，线性规划，二次锥规划，半定规划简介: lecture notes 线性规划，二次锥规划，半定规划例子: lecture notes 凸优化模型语言和算法软件，CVX, SDPT3, Mosek, CPLEX, Gruobi Prof. Boyd lecture notes on Disciplined convex programming and CVX read chapter 4 in in the book “Convex optimization” Introduction on Linear Programming (LP), read Chapter 1 in “Introduction to Linear Optimization” by Dimitris Bertsimas and John N. Tsitsiklis. Second-order Cone Programming (SOCP), read section 2 in “Second-order cone programming” Semidefinite Programming (SDP), read section 3 in “SDP-M-J-Todd” and section 2 in “SDP-Lieven-Boyd” The max cut paper by Goemans and Williamson 模型语言： CVX, YALMIP LP, SOCP, SDP典型算法软件: SDPT3, MOSEK, CPLEX, GUROBI NLP 典型算法软件: Ipopt, KNITRO Decision Tree for Optimization Software

第6周，10月29日，对偶理论, 凸优化最优性条件 Prof. Lieven Vandenberghe's lecture notes on duality read chapter 5 in in the book “Convex optimization” Lagrangian function, Lagrangian dual problem, examples max cut problem: dual of nonconvex problem, SDP relaxation: the dual of the dual duality using problem reformulation

第7周，11月3日，对偶理论, 凸优化最优性条件 Prof. Lieven Vandenberghe's lecture notes on duality

第8周，11月10日，梯度法和线搜索算法，最速下降法及其复杂度分析，线搜索算法，Barzilar-Borwein 方法 Prof. Lieven Vandenberghe's lecture notes on gradient methods Complexity analysis: Yu. Nesterov, Introductory Lectures on Convex Optimization. A Basic Course (2004), section 2.1. Line search: “Numerical Optimization”, Jorge Nocedal and Stephen Wright, chapter 3: 3.1, 3.5 Barzilar-Borwein Method: “Optimization Theory and Methods”, Wenyu Sun, Ya-Xiang Yuan, section 3.1.3 Matlab code on the BB method with nonmonotone line search

第8周，11月12日，梯度法和线搜索算法，最速下降法及其复杂度分析，线搜索算法，Barzilar-Borwein 方法

第9周，11月17日， 次梯度，次梯度算法 Prof. Lieven Vandenberghe's lecture notes on subgradient Prof. Lieven Vandenberghe's lecture notes on subgradient method

第10周，11月24日， 近似点算子的构造和性质 Prof. Lieven Vandenberghe's lecture notes on proximal mapping

第10周，11月26日， 期中考试

第11周，12月1日，近似点梯度法的构造和分析，条件梯度法, inertial proximal method Prof. Lieven Vandenberghe's lecture notes on proximal gradient method “Proximal Algorithms”, N. Parikh and S. Boyd, Foundations and Trends in Optimization, 1(3):123-231, 2014. 条件梯度法参考： 王奇超,文再文,蓝光辉,袁亚湘, 优化算法复杂度分析简介, (paper) Peter Ochs, Yunjin Chen, Thomas Brox, and Thomas Pock, iPiano: Inertial Proximal Algorithm for Nonconvex Optimization, SIAM J. IMAGING SCIENCES, Vol. 7, No. 2

第12周，12月8日， Nesterov加速算法和分析 Prof. Lieven Vandenberghe's lecture notes on fast proximal gradient method Prof. Lieven Vandenberghe's lecture notes on smoothing 王奇超,文再文,蓝光辉,袁亚湘, 优化算法复杂度分析简介, (paper) Paul Tseng, Approximation accuracy, gradient methods, and error bound for structured convex optimization, Math. Program., Ser. B (2010) 125:263–295 参考文献： Amir Beck, Marc Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems Weijie Su, Stephen Boyd, E. Candes, A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights

第12周，12月10日， 对偶分解 Prof. Lieven Vandenberghe's lecture notes on conjugate function Prof. Lieven Vandenberghe's lecture notes on dual decomposition

第13周，12月15日， 对偶近似点算法, PDHG Prof. Lieven Vandenberghe's lecture notes on dual proximal gradient method Lecture notes on PDHG

第14周，12月22日，mirror descent methods，近似点算法，增广拉格朗日函数法 Stephen Boyd John Duchi's lecture notes on mirror descent methods Prof. Lieven Vandenberghe's lecture notes on proximal point method

第14周，12月24日，Douglas-Rachford splitting, 交替方向乘子法及其变形，交替方向乘子法的构造 Lecture notes on ADMM Prof. Wotao Yin's lecture notes on ADMM “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers”, S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Foundations and Trends in Machine Learning, 3(1):1–122, 2011 Daniel O'Connor, Lieven Vandenberghey, On the equivalence of the primal-dual hybrid gradient method and Douglas-Rachford splitting

第15周，12月29日， Block Coordinate Descent Methods lecture notes on BCD Jérôme Bolte, Shoham Sabach, Marc Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems

第16周，1月5日， semi-smooth Newton methods lecture notes on semi-smooth methods

第16周，1月7日，Barrier functions, Path-following methods Prof. Lieven Vandenberghe's lecture notes on barrier functions Prof. Lieven Vandenberghe's lecture notes on path following methods Prof. Lieven Vandenberghe's lecture notes on primal-dual methods