# On the augmented subproblems within sequential methods for nonlinear programming

On the augmented subproblems within sequential methods for nonlinear programming In the context of sequential methods for solving general nonlinear programming problems, it is usual to work with augmented subproblems instead of the original ones. This paper addresses the theoretical reasoning behind handling the original subproblems by an augmentation strategy related to the differentiable reformulation of the $$\ell _1$$ ℓ 1 -penalized problem. Nevertheless, this paper is not concerned with the sequential method itself, but with the features about the original problem that can be inferred from the properties of the solution of the augmented problem. Moreover, no assumption is made upon the feasibility of the original problem, neither about the fulfillment of any constraint qualification, nor of any regularity condition, such as calmness. The convergence analysis of the involved sequences is presented, independent of the strategy employed to produce the iterates. Examples that elucidate the interrelations among the obtained results are also provided. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational and Applied Mathematics Springer Journals

# On the augmented subproblems within sequential methods for nonlinear programming

, Volume 36 (3) – Nov 3, 2015
18 pages

/lp/springer_journal/on-the-augmented-subproblems-within-sequential-methods-for-nonlinear-CAqiikddJt
Publisher
Springer International Publishing
Subject
Mathematics; Applications of Mathematics; Computational Mathematics and Numerical Analysis; Mathematical Applications in the Physical Sciences; Mathematical Applications in Computer Science
ISSN
0101-8205
eISSN
1807-0302
D.O.I.
10.1007/s40314-015-0291-7
Publisher site
See Article on Publisher Site

### Abstract

In the context of sequential methods for solving general nonlinear programming problems, it is usual to work with augmented subproblems instead of the original ones. This paper addresses the theoretical reasoning behind handling the original subproblems by an augmentation strategy related to the differentiable reformulation of the $$\ell _1$$ ℓ 1 -penalized problem. Nevertheless, this paper is not concerned with the sequential method itself, but with the features about the original problem that can be inferred from the properties of the solution of the augmented problem. Moreover, no assumption is made upon the feasibility of the original problem, neither about the fulfillment of any constraint qualification, nor of any regularity condition, such as calmness. The convergence analysis of the involved sequences is presented, independent of the strategy employed to produce the iterates. Examples that elucidate the interrelations among the obtained results are also provided.

### Journal

Computational and Applied MathematicsSpringer Journals

Published: Nov 3, 2015

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