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| + | ==== Convex Optimization ==== | ||
| + | |||
| == Course information == | == Course information == | ||
| - | * Instructor: Xiaohui Xie | + | * Instructor: Xiaohui Xie |
| - | * Meeting information: TT 3:30-4:50pm Room: ICS 180 | + | * Meeting information: TT 3:30-4:50pm Room: ICS 180 |
| - | * Office hours: TT after class | + | * Office hours: TT after class |
| == Prerequisites == | == Prerequisites == | ||
| - | * multivariate calculus and linear algebra | ||
| - | == Course Description == | + | * multivariate calculus and linear algebra |
| + | |||
| + | == Course Description == | ||
| This course will focus on formulating and solving convex optimization problems arising in engineering and science. Topics include: convex analysis, linear and quadratic programming, semidefinite programming, optimality conditions, duality theory, interior-point methods, subgradient methods, convex relaxation. | This course will focus on formulating and solving convex optimization problems arising in engineering and science. Topics include: convex analysis, linear and quadratic programming, semidefinite programming, optimality conditions, duality theory, interior-point methods, subgradient methods, convex relaxation. | ||
| == Textbook == | == Textbook == | ||
| - | * [http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf Convex Optimization] by Stephen Boyd and Lieven Vandenberghe, available online | + | * [[http://www.stanford.edu/boyd/cvxbook/bv_cvxbook.pdf|Convex Optimization]] by Stephen Boyd and Lieven Vandenberghe, available online |
| - | * [http://www.amazon.com/Analysis-Princeton-Mathematical-Tyrrell-Rockafellar/dp/0691080690 Convex Analysis] Rockafellar (suppl reference) | + | * [[http://www.amazon.com/Analysis-Princeton-Mathematical-Tyrrell-Rockafellar/dp/0691080690|Convex Analysis]] Rockafellar (suppl reference) |
| == Lectures == | == Lectures == | ||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/introduction.pdf Introduction] | + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/introduction.pdf|Introduction]] |
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/convex_sets.pdf|Convex Sets]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/convex_functions.pdf | Convex Functions]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/optimization_problems.pdf | Optimization Problems]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/optimality_conditions.pdf | Optimality Conditions]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/duality.pdf | Duality]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/unconstrained_opt.pdf | Unconstrained minimization]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/equality.pdf | Equality constrained minimization]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/interior.pdf | Interior-point methods]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/sdpintro.pdf | Introduction to Semidefinite Programming (SDP)]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/semidef_prog.pdf | SDP]] | ||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/convex_sets.pdf Convex Sets] | + | Modeling and application |
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/stochastic_subgradient_methods.pdf | Stochastic subgradient methods]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/stochastic_subgradient_methods_report.pdf | more details]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Multitask_Feature_Learning.pdf|Multitask feature learning]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Multitask_Feature_Learning_report.pdf | More details]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/FengJiang.pdf | Beamforming Optimization of MIMO Interference Network]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/color_constancy.pdf | Color Constancy]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/approximation.pdf | Approximation and fitting]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/struct_var_detection.pdf | Detecting genetic variation using fused Lasso]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Load_balancing_ConvOpt.pdf | Load balancing on a heterogeneous cluster]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/graph_isomorphism.pdf | Detecting graph isomorphism]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Load_balancing_ConvOpt.pdf | Load balancing on a heterogeneous cluster]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Modeling_Marketing_Promotion_Choices.pdf | Modeling marketing promotion choices]] | ||
| + | * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/PatrickFlynn.pdf | Conjugate gradient method]] | ||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/convex_functions.pdf Convex Functions] | ||
| - | |||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/optimization_problems.pdf Optimization Problems] | ||
| - | |||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/optimality_conditions.pdf Optimality Conditions] | ||
| - | |||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/duality.pdf Duality] | ||
| - | |||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/unconstrained_opt.pdf Unconstrained minimization] | ||
| - | |||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/equality.pdf Equality constrained minimization] | ||
| - | |||
| - | * [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/interior.pdf Interior-point methods] | ||
| - | |||
| - | * Semi-definite programming | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/sdpintro.pdf Introduction to Semidefinite Programming (SDP)] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/semidef_prog.pdf SDP] | ||
| - | |||
| - | * Modeling and application | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/stochastic_subgradient_methods.pdf Stochastic subgradient methods] | ||
| - | *** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/stochastic_subgradient_methods_report.pdf more details] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Multitask_Feature_Learning.pdf Multitask feature learning] | ||
| - | *** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Multitask_Feature_Learning_report.pdf More details] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/FengJiang.pdf Beamforming Optimization of MIMO Interference Network] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/color_constancy.pdf Color Constancy] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/approximation.pdf Approximation and fitting] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/struct_var_detection.pdf Detecting genetic variation using fused Lasso] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Load_balancing_ConvOpt.pdf Load balancing on a heterogeneous cluster] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/graph_isomorphism.pdf Detecting graph isomorphism] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Load_balancing_ConvOpt.pdf Load balancing on a heterogeneous cluster] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Modeling_Marketing_Promotion_Choices.pdf Modeling marketing promotion choices] | ||
| - | ** [http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/PatrickFlynn.pdf Conjugate gradient method] | ||
| - | |||
| - | == [[ConvexOptFall2010Projects | Projects]] == | ||
| == Key dates == | == Key dates == | ||
| - | * Final exam: Mar 15, 4:00-6:00pm (Bring one examination blue book!) | + | * Final exam: Mar 15, 4:00-6:00pm (Bring one examination blue book!) |
| - | * Final project due: Mar 18, 5pm, hard copy in Bren Hall 4058 | + | * Final project due: Mar 18, 5pm, hard copy in Bren Hall 4058 |
| == Exercise == | == Exercise == | ||
| - | + | * Convex sets: 2.1, 2.9, 2.12, 2.15, 2.23, 2.24, 2.33 (from the textbook) | |
| - | * Convex sets: 2.1, 2.9, 2.12, 2.15, 2.23, 2.24, 2.33 (from the textbook) | + | * Convex functions: 3.2, 3.15, 3.16, 3.36, 3.42 |
| - | + | * Convex problems; 4.1, 4.65 | |
| - | * Convex functions: 3.2, 3.15, 3.16, 3.36, 3.42 | + | * Duality: 5.1, 5.13, 5.38, 5.42 |
| - | + | ||
| - | * Convex problems; 4.1, 4.65 | + | |
| - | + | ||
| - | * Duality: 5.1, 5.13, 5.38, 5.42 | + | |