Welcome to Cvx-Learning’s documentation!

I have followed the full courses in internet of the Stanford open classes. With the notes as following :

• Linear Dynamtic System EE263
• Convex Optimziation I EE364A
• Convex Optimziation II EE364B

And this pages contain my learning in more detail aspects.

Contents:

• Semidefinite Programming
  • 1. Introduction
  • 2. Examples
    • 2.1 QCQP
    • 2.2 Maximum eigenvalues and matrix norm minimization
    • 2.3 Logarithmic Chebychev approximation
    • 2.4 Structural optimziation
    • 2.5 Pattern separation by ellipsoid
    • 2.6 Statistics
    • 2.7 Control and System theory
  • 3. Duality
    • 3.1 Strong Duality
    • 3.2 Optimal Condition
    • 3.3 Primal-Dual
  • 4. The Central Path
    • 4.1 Barrier Function for a linear matrix inequality
    • 4.2 Analytic center
    • 4.4 Central Path: Objective
    • 4.5 Central Path: Duality gap
  • 5. Primal-dual potential reduction methods
    • 5.1 General Description
    • 5.2 Potential reduction method 1
    • 5.3 Potential reduction method 2
    • 5.4 Potential reduction method 3
    • 5.5 Plane search
    • 5.6 Numerical examples
  • 6. Phase I and Phase I-II methods
    • 6.1 Gig-M method
    • 6.2 Others
• Proximal Algorithms
  • Monotone Operators
    • 1. Some Backgrounds
    • 2. Monotone operator
    • 3. Variational Inequalities
    • 4. Lagrangian
    • 5. Algorithm
    • 6. Stop Criteria
    • 7. Applications
    • 8. Convergence
  • 1. Proximal Algorithms Introduction
    • 1.1 Definitions
    • 1.2 Generalized projections
    • 1.3 Gradient step
    • 1.4 Fixed point
    • 1.5 Advantages
    • 1.6 Review convex cones
  • 2. Properties
    • 2.1 Separable sum
    • 2.2 Basic operations
    • 2.3 Proximal average
    • 2.4 Moreau decomposition
  • 3. Interpretations
    • 3.1 Moreau-Yosida regularization
    • 3.2 Resolvent of subdifferential operator
    • 3.3 Modified gradient step
    • 3.4 Trust region problem
  • 4. Proximal Algorithms
    • 4.1 Proximal minimization
    • 4.2 Proximal gradient method
    • 4.3 Accelerated proximal gradient method
    • 4.3 Alternating direction method of multipliers
    • 4.4 LM interpretations
    • 4.5 The augmented Largrangian method
  • 5. Parallel and Distributed Algorithms
  • 6. Evaluating Proximal Operators
    • 6.1 Generic methods
    • 6.2 Polyhedra
    • 6.3 Cones
    • 6.5 Norms and norm balls
  • 7. Applications
    • 7.1 Lasso
    • 7.2 Matrix decomposition
    • 7.3 Multi-period portfolio optimization
    • 7.4 Stochastic optimization
  • 8. Conclusions
• ADMM
  • 1. Introduction
    • 1.1 Goal
    • 1.2 Closely Related Algorithms
    • 1.3 BluePrint
    • 1.4 Interpretation as tatonnement process
  • 2. Precursors
    • 2.1 Dual Ascent
    • 2.2 Dual Decomposition
    • 2.3 Augmented Lagrangians and the Method of Multipliers
  • 3. Alternating Direction Method of Multipliers
    • 3.1 Algorithm
    • 3.2 Scaled form
    • 3.3 Optimality Conditions and Stopping Criterion
    • 3.4 Varying Penalty Parameter
  • 4. General Pattern
    • 4.1 Proximity Operator
    • 4.2 Quadratic Objective Function
    • 4.3 Smooth Objective Terms
    • 4.4 Decomposition
  • 5. Constrained Convex Optimization
    • 5.1 Quadratic Programming
    • 5.2 Test LP
    • 5.3 Test QP
    • 5.4 Polyhedra Intersection
  • 6. L1 Norm Problems
    • 6.1 Huber Fitting
    • 6.2 Basis pursuit problem
    • 6.3 L1 Regulaized Loss
    • 6.4 Lasso
    • 6.5 Sparse Inverse Covariance Selection
    • 6.6 Total Variation Reconstruction
  • 7. Consensus and Sharing
    • 7.1 Global Variable Consensus
    • 7.2 Sharing
  • 8. Distributed Model Fitting
    • 8.1 Examples
    • 8.2 Splitting across examples
    • 8.3 Splitting across Features
  • 9. Nonconvex Problem
    • 9.1 Nonconvex Constraints
    • 9.2 Bi-convex Problems
  • 10. Implementation
    • 10.1 Abstract Implementation
    • 10.2 MPI
    • 10.3 Graph Computing Frameworks
    • 10.4 MapReduce
  • 11. Numerical Examples
• Paper Reads
  • CVX based SLAM related algorithms
    • 1. Banch and Bound
    • 2. Lagrangian Duality
    • 3. TEASER++
  • Douglas-Rachford Splitting Algorithm
    • 1. Splitting algorithms
    • 2. Monotonicity
  • Augmented Lagrangian and Proximal Point Algorithm
    • 1. Proximal point algorithm for P : primal
    • 2. Proximal point algorithm for D : dual
    • 3. Proximal point algorithm for Convex-concave Lagrangian
  • On the Unification of Line Processes, Outlier Rejection, and Robust Statistics
    • 1. L1 Heuristic
    • 2. Line Process
    • 3. Robust Statistics
    • 4. Unifying Robust Estimation and Outlier Processes
    • 5. Adding Spatial Interactions
  • Solving TV via ADMM
    • 1. Introduction
    • 2. ADMM
    • 3. Application TV-L2
    • 3. Application TV-LP
    • 4. Image Decomposition
  • Primal-Dual Mumford-Shah
    • 1. Mumford-Shah Functional
    • 2. Convex Relaxation
    • 3. First-order Primal-Dual

Indices and tables

• Index
• Module Index
• Search Page

contact me

gggliuye@gmail.com