Simple unification and Application of convex optimization and contraction Algorithms

From: partition sor bingsheng he

Http://math.nju.edu.cn /~ Hebma/

 

 

Simple unification and Application of convex optimization and contraction algorithms-Algorithm Research strives for the beauty of Mathematics

　

Preface, contents and summaries

　

Part 1: solution to monotonic Variational Inequality

　

1st. variational inequality as a unified expression model for multiple problems

　

2nd. Projection contraction algorithms for the three basic inequalities and Variational Inequalities

　

3rd. A unified framework of the monotonic variational inequality contraction Algorithm

　

Part 2: Solution to the convex optimization problem {min f (x) | Ax = B, X in X}

　

4th lecture. PPA algorithm customized for Linear Constrained Convex Optimization and Its Application

　

5th. Linear Constrained Convex Optimization Problem Based on the contraction algorithm of relaxed PPA

　

6th. PPA and relaxed PPA contraction algorithms for Linear Constrained Convex Optimization and expansion problems

　

7th lecture. PPA contraction Algorithm Based on Augmented Laplace Multiplier

　

Part 3: Projection gradient-based shrinkage algorithm

　

8th. Gradient Projection-based convex optimization contraction algorithm and Descent Algorithm

　

9th. Adaptive Method Based on Dual rise for Linear Constrained Convex Optimization

　

10th. Adaptive projection contraction Algorithm for Linear Constrained monotonic Variational Inequality

 

Part 4: convex optimization {min f (x) + g (y) | Ax + by = B, X in X, Y in y} alternating direction method

　

Lecture 11th. Alternate Direction Method for Structural Optimization

　

12th lecture. Linear alternating direction contraction Algorithm

　

13th. Define the alternating direction method in the PPA sense

　

14th. Define the linear alternating direction method for the meaning of PPA

　

Part 5: Splitting Method with simple correction for Convex Optimization of multiple detachable Operators

　

15th lecture. Parallel split-wise augmented Laplace Multiplier Method for Convex Optimization of three detachable Operators

　

16th lecture. Alternating forward method with slightly changed convex optimization of three detachable Operators

Lecture 17th. alternate direction contraction algorithm brought back by convex optimization of multiple detachable Operators

18th lecture. Multiple separated operator Convex Optimization back-to-line alternating direction method