TY - GEN
T1 - Complexity certifications of first-order inexact lagrangian methods for general convex programming
T2 - International Conference on Optimisation-based Control and Estimation, 2014
AU - Necoara, Ion
AU - Patrascu, Andrei
AU - Nedić, Angelia
N1 - Funding Information:
First author’s work has been founded by UEFISCDI, project MoCOBiDS (PN II–RU–TE 2014), no. 176/01.10.2015. Second author’s work has been funded by the Sectoral Operational Programme Human Resources Development 2007–2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/134398. Third author’s work has been funded by the Office of Naval Research under grant no. N00014-12-1-0998.
Publisher Copyright:
© Springer International Publishing Switzerland 2015.
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.
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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
T3 - Lecture Notes in Control and Information Sciences
SP - 3
EP - 26
BT - Developments in Model-Based Optimization and Control
A2 - Grancharova, Alexandra
A2 - Olaru, Sorin
A2 - Pereira, Fernando Lobo
PB - Springer Verlag
Y2 - 1 November 2013
ER -