4,918 research outputs found
Primal-dual extragradient methods for nonlinear nonsmooth PDE-constrained optimization
We study the extension of the Chambolle--Pock primal-dual algorithm to
nonsmooth optimization problems involving nonlinear operators between function
spaces. Local convergence is shown under technical conditions including metric
regularity of the corresponding primal-dual optimality conditions. We also show
convergence for a Nesterov-type accelerated variant provided one part of the
functional is strongly convex.
We show the applicability of the accelerated algorithm to examples of inverse
problems with - and -fitting terms as well as of
state-constrained optimal control problems, where convergence can be guaranteed
after introducing an (arbitrary small, still nonsmooth) Moreau--Yosida
regularization. This is verified in numerical examples
Deductive Verification of Parallel Programs Using Why3
The Message Passing Interface specification (MPI) defines a portable
message-passing API used to program parallel computers. MPI programs manifest a
number of challenges on what concerns correctness: sent and expected values in
communications may not match, resulting in incorrect computations possibly
leading to crashes; and programs may deadlock resulting in wasted resources.
Existing tools are not completely satisfactory: model-checking does not scale
with the number of processes; testing techniques wastes resources and are
highly dependent on the quality of the test set.
As an alternative, we present a prototype for a type-based approach to
programming and verifying MPI like programs against protocols. Protocols are
written in a dependent type language designed so as to capture the most common
primitives in MPI, incorporating, in addition, a form of primitive recursion
and collective choice. Protocols are then translated into Why3, a deductive
software verification tool. Source code, in turn, is written in WhyML, the
language of the Why3 platform, and checked against the protocol. Programs that
pass verification are guaranteed to be communication safe and free from
deadlocks.
We verified several parallel programs from textbooks using our approach, and
report on the outcome.Comment: In Proceedings ICE 2015, arXiv:1508.0459
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