We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x
1, . . . , x

 N
 ) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iterates to a stationary point is shown when either f is pseudoconvex in every pair of coordinate blocks from among N-1 coordinate blocks or f has at most one minimum in each of N-2 coordinate blocks. If f is quasiconvex and hemivariate in every coordinate block, then the assumptions of continuity of f and compactness of the level set may be relaxed further. These results are applied to derive new (and old) convergence results for the proximal minimization algorithm, an algorithm of Arimoto and Blahut, and an algorithm of Han. They are applied also to a problem of blind source separation.

http://gautampendse.com/software/lasso/webpage/Tseng2001.pdf

Convergence of a block coordinate descent method for nondifferentiable minimization

This paper describes a modification of differential dynamic programming (DDP) which makes that technique applicable to certain constrained sequential decision problems such as multireservoir control problems discussed in the hydrology literature. The authors contend that the method proffered here is superior to available alternatives. This belief is supported by analysis (wherein it transpires that constrained DDP does not suffer the ‘curse of dimensionality’ and requires no discretization) and computational experimentation (wherein DDP is found to quickly locate solutions of 4-reservoir problems introduced by other investigations as well as the solution of a 10-reservoir problem thought to be beyond the capability of alternative methods).

Constrained Differential Dynamic Programming and Its Application to Multireservoir Control

This paper presents an algorithm based on the principle of progressive optimality for determining the optimal short-term scheduling of multireservoir power systems; the method takes into account water head variations, spilling, and time delays between upstream and downstream reservoirs. The method is computationally efficient and has minimal storage requirements. The convergence is monotonic and a global solution is reached. Contrary to dynamic programing, the state variables do not have to be discretized with this method. An example consisting of four hydroplants in series is solved, and the results are presented.

Optimal short-term hydro scheduling from the principle of progressive optimality

A parallel dynamic programming algorithm for multi-reservoir system optimization

Computational aspects of discrete-time optimal control

A dynamic programming successive approximations technique with convergence proofs

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

R.E. Larson

Author Tools

Chat about Author

Papers

A dynamic programming successive approximations technique with convergence proofs