18,062 research outputs found
OSQP: An Operator Splitting Solver for Quadratic Programs
We present a general-purpose solver for convex quadratic programs based on
the alternating direction method of multipliers, employing a novel operator
splitting technique that requires the solution of a quasi-definite linear
system with the same coefficient matrix at almost every iteration. Our
algorithm is very robust, placing no requirements on the problem data such as
positive definiteness of the objective function or linear independence of the
constraint functions. It can be configured to be division-free once an initial
matrix factorization is carried out, making it suitable for real-time
applications in embedded systems. In addition, our technique is the first
operator splitting method for quadratic programs able to reliably detect primal
and dual infeasible problems from the algorithm iterates. The method also
supports factorization caching and warm starting, making it particularly
efficient when solving parametrized problems arising in finance, control, and
machine learning. Our open-source C implementation OSQP has a small footprint,
is library-free, and has been extensively tested on many problem instances from
a wide variety of application areas. It is typically ten times faster than
competing interior-point methods, and sometimes much more when factorization
caching or warm start is used. OSQP has already shown a large impact with tens
of thousands of users both in academia and in large corporations
Progressive construction of a parametric reduced-order model for PDE-constrained optimization
An adaptive approach to using reduced-order models as surrogates in
PDE-constrained optimization is introduced that breaks the traditional
offline-online framework of model order reduction. A sequence of optimization
problems constrained by a given Reduced-Order Model (ROM) is defined with the
goal of converging to the solution of a given PDE-constrained optimization
problem. For each reduced optimization problem, the constraining ROM is trained
from sampling the High-Dimensional Model (HDM) at the solution of some of the
previous problems in the sequence. The reduced optimization problems are
equipped with a nonlinear trust-region based on a residual error indicator to
keep the optimization trajectory in a region of the parameter space where the
ROM is accurate. A technique for incorporating sensitivities into a
Reduced-Order Basis (ROB) is also presented, along with a methodology for
computing sensitivities of the reduced-order model that minimizes the distance
to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced
optimization framework is applied to subsonic aerodynamic shape optimization
and shown to reduce the number of queries to the HDM by a factor of 4-5,
compared to the optimization problem solved using only the HDM, with errors in
the optimal solution far less than 0.1%
Compressive sensing adaptation for polynomial chaos expansions
Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of
the underlying Gaussian germ. Several rotations have been proposed in the
literature resulting in adaptations with different convergence properties. In
this paper we present a new adaptation mechanism that builds on compressive
sensing algorithms, resulting in a reduced polynomial chaos approximation with
optimal sparsity. The developed adaptation algorithm consists of a two-step
optimization procedure that computes the optimal coefficients and the input
projection matrix of a low dimensional chaos expansion with respect to an
optimally rotated basis. We demonstrate the attractive features of our
algorithm through several numerical examples including the application on
Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE
scramjet engine.Comment: Submitted to Journal of Computational Physic
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