# On $${\epsilon}$$ -solutions for convex optimization problems with uncertainty data

On $${\epsilon}$$ -solutions for convex optimization problems with uncertainty data We consider $${\epsilon}$$ -solutions (approximate solutions) for a robust convex optimization problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we establish an optimality theorem and duality theorems for $${\epsilon}$$ -solutions for the robust convex optimization problem. Moreover, we give an example illustrating the duality theorems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# On $${\epsilon}$$ -solutions for convex optimization problems with uncertainty data

, Volume 16 (3) – Jun 26, 2012
18 pages

/lp/springer_journal/on-epsilon-solutions-for-convex-optimization-problems-with-uncertainty-Rp5D37Ztwh
Publisher
Springer Journals
Subject
Mathematics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0186-4
Publisher site
See Article on Publisher Site

### Abstract

We consider $${\epsilon}$$ -solutions (approximate solutions) for a robust convex optimization problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we establish an optimality theorem and duality theorems for $${\epsilon}$$ -solutions for the robust convex optimization problem. Moreover, we give an example illustrating the duality theorems.

### Journal

PositivitySpringer Journals

Published: Jun 26, 2012

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations