Complexity certifications of first-order inexact lagrangian methods for general convex programming: Application to real-time MPC

Ion Necoara, Andrei Patrascu, Angelia Nedich

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

In this chapter, we derive the computational complexity certifications of first-order inexact dual methods for solving general smooth constrained convex problems which can arise in real-time applications, such as model predictive control. When it is difficult to project on the primal constraint set described by a collection of general convex functions, we use the Lagrangian relaxation to handle the complicated constraints and then, we apply dual (fast) gradient algorithms based on inexact dual gradient information for solving the corresponding dual problem. The iteration complexity analysis is based on two types of approximate primal solutions: the primal last iterate and an average of primal iterates.We provide sublinear computational complexity estimates on the primal suboptimality and constraint (feasibility) violation of the generated approximate primal solutions. In the final part of the chapter, we present an open-source quadratic optimization solver, referred to as DuQuad, for convex quadratic programs and for evaluation of its behavior. The solver contains the C-language implementations of the analyzed algorithms.

Original languageEnglish (US)
Title of host publicationDevelopments in Model-Based Optimization and Control: Distributed Control and Industrial Applications
PublisherSpringer Verlag
Pages3-26
Number of pages24
Volume464
ISBN (Print)9783319266855
DOIs
StatePublished - 2015
Externally publishedYes
EventInternational Conference on Optimisation-based Control and Estimation, 2014 - Paris, France
Duration: Nov 1 2013 → …

Publication series

NameLecture Notes in Control and Information Sciences
Volume464
ISSN (Print)01708643

Other

OtherInternational Conference on Optimisation-based Control and Estimation, 2014
CountryFrance
CityParis
Period11/1/13 → …

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certification
programming
predictive model
language
evaluation
time

ASJC Scopus subject areas

  • Library and Information Sciences

Cite this

Necoara, I., Patrascu, A., & Nedich, A. (2015). Complexity certifications of first-order inexact lagrangian methods for general convex programming: Application to real-time MPC. In Developments in Model-Based Optimization and Control: Distributed Control and Industrial Applications (Vol. 464, pp. 3-26). (Lecture Notes in Control and Information Sciences; Vol. 464). Springer Verlag. https://doi.org/10.1007/978-3-319-26687-9_1

Complexity certifications of first-order inexact lagrangian methods for general convex programming : Application to real-time MPC. / Necoara, Ion; Patrascu, Andrei; Nedich, Angelia.

Developments in Model-Based Optimization and Control: Distributed Control and Industrial Applications. Vol. 464 Springer Verlag, 2015. p. 3-26 (Lecture Notes in Control and Information Sciences; Vol. 464).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Necoara, I, Patrascu, A & Nedich, A 2015, Complexity certifications of first-order inexact lagrangian methods for general convex programming: Application to real-time MPC. in Developments in Model-Based Optimization and Control: Distributed Control and Industrial Applications. vol. 464, Lecture Notes in Control and Information Sciences, vol. 464, Springer Verlag, pp. 3-26, International Conference on Optimisation-based Control and Estimation, 2014, Paris, France, 11/1/13. https://doi.org/10.1007/978-3-319-26687-9_1
Necoara I, Patrascu A, Nedich A. Complexity certifications of first-order inexact lagrangian methods for general convex programming: Application to real-time MPC. In Developments in Model-Based Optimization and Control: Distributed Control and Industrial Applications. Vol. 464. Springer Verlag. 2015. p. 3-26. (Lecture Notes in Control and Information Sciences). https://doi.org/10.1007/978-3-319-26687-9_1
Necoara, Ion ; Patrascu, Andrei ; Nedich, Angelia. / Complexity certifications of first-order inexact lagrangian methods for general convex programming : Application to real-time MPC. Developments in Model-Based Optimization and Control: Distributed Control and Industrial Applications. Vol. 464 Springer Verlag, 2015. pp. 3-26 (Lecture Notes in Control and Information Sciences).
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