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9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1周，9月10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，9月16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3周，9月23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.mDemo: Sparse matrix-dense vector products using intel MKL BLAS (Basic Linear Algebra Subprograms)LAPACK (Linear Algebra PACKage)Intel Math Kernel Library – DocumentationCall LAPACK and BLAS Functions in Matlab
第3周，9月24日，典型的凸优化问题： lecture notes read chapter 4 in in the book “Convex optimization”
第4周，9月30日，国庆节放假
第5周，10月7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 CVXread 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, KNITRODecision Tree for Optimization Software
第5周，10月8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, examplesmax cut problem: dual of nonconvex problem, SDP relaxation: the dual of the dualduality using problem reformulation
第6周，10月14日，对偶理论, 凸优化最优性条件 Prof. Lieven Vandenberghe's lecture notes on duality
第7周，10月21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 methodsComplexity 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, 3.5Barzilar-Borwein Method: “Optimization Theory and Methods”, Wenyu Sun, Ya-Xiang Yuan, section 3.1.3Matlab code on the BB method with nonmonotone line search
第7周，10月22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8周，10月28日， 次梯度 Prof. Lieven Vandenberghe's lecture notes on subgradient
第9周，11月4日， 次梯度算法 Prof. Lieven Vandenberghe's lecture notes on subgradient method
第9周，11月5日， 期中考试
第10周，11月11日，近似点算子的构造和性质Prof. Lieven Vandenberghe's lecture notes on proximal mapping
第11周，11月18日，近似点梯度法的构造和分析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.
第11周，11月19日， Nesterov加速算法和分析 Prof. Lieven Vandenberghe's lecture notes on fast proximal gradient methodProf. 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 errorbound 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 ProblemsWeijie Su, Stephen Boyd, E. Candes, A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
第12周，11月25日， 对偶分解 Prof. Lieven Vandenberghe's lecture notes on conjugate functionProf. Lieven Vandenberghe's lecture notes on dual decomposition
第13周，12月2日， 对偶近似点算法，条件梯度法, inertial proximal method Prof. Lieven Vandenberghe's lecture notes on dual proximal gradient method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13周，12月3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 methodsProf. Lieven Vandenberghe's lecture notes on proximal point method
第14周，12月9日，Douglas-Rachford splitting and ADMM Prof. Lieven Vandenberghe'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 andDouglas-Rachford splitting
第15周，12月16日， 交替方向乘子法及其变形，交替方向乘子法的构造, Distributed ADMM Prof. Wotao Yin's lecture notes on ADMM
第15周，12月17日， Block Coordinate Descent Methods, semi-smooth Newton methods lecture notes on BCD lecture notes on semi-smooth methods Jérôme Bolte, Shoham Sabach, Marc Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems
第16周，12月23日，Barrier functions, Path-following methods Prof. Lieven Vandenberghe's lecture notes on barrier functionsProf. Lieven Vandenberghe's lecture notes on path following methodsProf. Lieven Vandenberghe's lecture notes on primal-dual methods