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 language | English (US) |
|---|---|
| Title of host publication | Developments in Model-Based Optimization and Control: Distributed Control and Industrial Applications |
| Publisher | Springer Verlag |
| Pages | 3-26 |
| Number of pages | 24 |
| Volume | 464 |
| ISBN (Print) | 9783319266855 |
| DOIs | |
| State | Published - 2015 |
| Externally published | Yes |
| Event | International Conference on Optimisation-based Control and Estimation, 2014 - Paris, France Duration: Nov 1 2013 → … |
Publication series
| Name | Lecture Notes in Control and Information Sciences |
|---|---|
| Volume | 464 |
| ISSN (Print) | 01708643 |
Other
| Other | International Conference on Optimisation-based Control and Estimation, 2014 |
|---|---|
| Country | France |
| City | Paris |
| Period | 11/1/13 → … |
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ASJC Scopus subject areas
- Library and Information Sciences
Cite this
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 proceeding › Conference contribution
}
TY - GEN
T1 - Complexity certifications of first-order inexact lagrangian methods for general convex programming
T2 - Application to real-time MPC
AU - Necoara, Ion
AU - Patrascu, Andrei
AU - Nedich, Angelia
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84954168622&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84954168622&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-26687-9_1
DO - 10.1007/978-3-319-26687-9_1
M3 - Conference contribution
AN - SCOPUS:84954168622
SN - 9783319266855
VL - 464
T3 - Lecture Notes in Control and Information Sciences
SP - 3
EP - 26
BT - Developments in Model-Based Optimization and Control: Distributed Control and Industrial Applications
PB - Springer Verlag
ER -