@article{KochBertholdPedersenetal.2022, author = {Koch, Thorsten and Berthold, Timo and Pedersen, Jaap and Vanaret, Charlie}, title = {Progress in mathematical programming solvers from 2001 to 2020}, volume = {10}, journal = {EURO Journal on Computational Optimization}, doi = {10.1016/j.ejco.2022.100031}, pages = {100031}, year = {2022}, abstract = {This study investigates the progress made in lp and milp solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving lp/milp, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for lp and around 50 for milp, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time.}, language = {en} } @article{KiesslingLeyfferVanaret2025, author = {Kießling, David and Leyffer, Sven and Vanaret, Charlie}, title = {A Unified Funnel Restoration SQP Algorithm}, journal = {Mathematical Programming B}, doi = {10.1007/s10107-025-02284-3}, year = {2025}, abstract = {We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of basic algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.}, language = {en} } @article{Vanaret2024, author = {Vanaret, Charlie}, title = {Interval constraint programming for globally solving catalog-based categorical optimization}, volume = {89}, journal = {Journal of Global Optimization}, arxiv = {http://arxiv.org/abs/2104.03652}, doi = {10.1007/s10898-023-01362-0}, pages = {457 -- 476}, year = {2024}, abstract = {In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require any modeling effort from the user. A novel catalog-based contractor (or filtering operator) guarantees consistency between the categorical properties and the existing catalog items. This results in an intuitive and generic approach that is exact, rigorous (robust to roundoff errors) and can be easily implemented in an off-the-shelf interval-based continuous solver that interleaves branching and constraint propagation. We demonstrate the validity of the approach on a numerical problem in which a categorical variable is described by a two-dimensional property space. A Julia prototype is available as open-source software under the MIT license.}, language = {en} }