1,944 research outputs found
Improved analysis of algorithms based on supporting halfspaces and quadratic programming for the convex intersection and feasibility problems
This paper improves the algorithms based on supporting halfspaces and
quadratic programming for convex set intersection problems in our earlier paper
in several directions. First, we give conditions so that much smaller quadratic
programs (QPs) and approximate projections arising from partially solving the
QPs are sufficient for multiple-term superlinear convergence for nonsmooth
problems. Second, we identify additional regularity, which we call the second
order supporting hyperplane property (SOSH), that gives multiple-term quadratic
convergence. Third, we show that these fast convergence results carry over for
the convex inequality problem. Fourth, we show that infeasibility can be
detected in finitely many operations. Lastly, we explain how we can use the
dual active set QP algorithm of Goldfarb and Idnani to get useful iterates by
solving the QPs partially, overcoming the problem of solving large QPs in our
algorithms.Comment: 27 pages, 2 figure
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
Construction of power flow feasibility sets
We develop a new approach for construction of convex analytically simple
regions where the AC power flow equations are guaranteed to have a feasible
solutions. Construction of these regions is based on efficient semidefinite
programming techniques accelerated via sparsity exploiting algorithms.
Resulting regions have a simple geometric shape in the space of power
injections (polytope or ellipsoid) and can be efficiently used for assessment
of system security in the presence of uncertainty. Efficiency and tightness of
the approach is validated on a number of test networks
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