A generic framework for the solution of PDE-constrained optimisation problems based on the FEniCS system is presented. Its main features are an intuitive mathematical interface, a high degree of automation, and an efficient implementation of the generated adjoint model. The framework is based upon the extension of a domain-specific language for variational problems to cleanly … Read more
Several variations of index selection rules for simplex type algorithms for linear programming, like the Last-In-First-Out or the Most-Often-Selected-Variable are rules not only theoretically finite, but also provide significant flexibility in choosing a pivot element. Based on an implementation of the primal simplex and the monotonic build-up (MBU) simplex method, the practical benefit of the … Read more
We study the runtime performance of three types of random-key genetic algorithms: the unbiased algorithm of Bean (1994); the biased algorithm of Gonçalves and Resende (2011); and a greedy version of Bean’s algorithm on 12 instances from four types of covering problems: general-cost set covering, Steiner triple covering, general-cost set K-covering, and unit-cost covering by … Read more
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite … Read more
VSDP is a software package that is designed for the computation of verified results in conic programming. The current version of VSDP supports the constraint cone consisting of the product of semidefinite cones, second-order cones and the nonnegative orthant. It provides functions for computing rigorous error bounds of the true optimal value, verified enclosures of … Read more
In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex function. The theoretical speedup, as compared to the serial method, and referring to the number of iterations needed … Read more
The \emph{interval bounded generalized trust region subproblem} (GTRS) consists in minimizing a general quadratic objective, $q_0(x) \rightarrow \min$, subject to an upper and lower bounded general quadratic constraint, $\ell \leq q_1(x) \leq u$. This means that there are no definiteness assumptions on either quadratic function. We first study characterizations of optimality for this \emph{implicitly} convex … Read more
This paper studies an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale separable convex programming problems. Unlike the exact versions considered in the literature, we propose to solve the primal subproblems inexactly up to a given accuracy. This leads to an inexactness of the gradient vector and the Hessian … Read more
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our algorithm is based on block coordinate descent updates in parallel and has a very simple iteration. We prove (sub)linear rate of … Read more
This position paper reflects on the generalization of adaptive methods for Constraint Programming (CP) solving mechanisms, and suggests the use of application-oriented descriptions as a means to broaden CP adoption in the industry. We regard as an adaptive method any procedure that modifies the behavior of the solving process according to previous experience gathered from … Read more