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Optimal Control with Minimum Total Variation

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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Kaya, Yalcin C.

Formal Metadata

Title

Optimal Control with Minimum Total Variation

Title of Series

Splitting Algorithms, Modern Operator Theory, and Applications (17w5030)

Number of Parts

30

Author

Kaya, Yalcin C.

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.14288/1.0364466 (DOI)

Publisher

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Release Date

Language

Content Metadata

Subject Area

Computer Science Mathematics

Genre

Workshop/Interactive Format Lecture

Abstract

We consider optimal control problems where the aim is to minimize the total variation in the control variables in addition to a general objective functional, resulting in a multi-objective optimal control problem. We study an illustrative convex problem, which appears in a simple form, and obtain asymptotic results for the challenging case when only the total variation is to be minimized. We also discuss problems which are in a more general form.

Series

Splitting Algorithms, Modern Operator Theory, and Applications (17w5030)23 / 30

1

33:19

Nesterov accelerated gradient method in the subcritical case α≤ 3

2

25:38

Iteratively re-weighted least squares for Sums of Convex Functions

3

39:47

On the Glaeser-Whitney extension problem

4

35:01

Golden Ratio Algorithms for Variational Inequalities

5

27:30

ADMM for monotone operators: convergence analysis and rates

6

29:28

The Douglas-Rachford method for finding intersections of hypersurfaces

7

35:48

The Inverse Function Theorems of Lawrence M. Graves

8

33:14

A Unified Approach to Error Bounds for Structured Convex Optimization Problems

9

32:04

MODULI OF REGULARITY AND RATES OF CONVERGENCE FOR FEJER MONOTONE SEQUENCES

10

37:43

Parallel, Block-Iterative, Primal-Dual Monotone Operator Splitting

11

32:01

Minimization of quadratic functions on convex sets without asymptotes

12

37:38

On the Douglas–Rachford operator in the (possibly) inconsistent case and related progress

13

36:15

An inertial forward-backward method for solving vector optimization problems

14

35:33

On Decomposing the Proximal Map

15

32:20

Hierarchical Convex Optimization with Proximal Splitting Operators

16

36:02

Sharp Penalty Mapping Approach to Approximate Solution of Monotone Variational Inequalities

17

36:18

Quasidense multifunctions

18

26:00

A parameterized Douglas-Rachford algorithm

19

39:46

A general double-proximal gradient algorithm for d.c. programming

20

37:57

The flow limit of reflect-reflect-relax

21

35:59

Sharp Contraction Factors for the Douglas-Rachford Operator

22

31:55

A projection algorithm for non-monotone variational inequalities

23

36:29

Optimal Control with Minimum Total Variation

24

35:06

Modifying the Douglas-Rachford algorithm to solve best approximation problems

25

39:17

ProxToolbox: A Labortatory for Quantitative Convergence Analysis of Picard Iterations

26

38:06

Pointwise and ergodic convergence rates of a variable metric proximal ADMM

27

39:19

Pointwise Asymptotic Stability of a Continuum of Equilibria

28

23:40

Convex Feasibility via Monotropic Programming

29

33:05

Improved pointwise iteration-complexity of a regularized ADMM

30

36:26

Error bounds and convergence of proximal methods for composite minimization

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