Mathematical Programming Computation
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A triangulation and fill-reducing initialization procedure for the simplex algorithm
Mathematical Programming Computation - Tập 13 - Trang 491-508 - 2020
The computation of an initial basis is of great importance for simplex
algorithms since it determines to a large extent the number of iterations and
the computational effort needed to solve linear programs. We propose three
algorithms that aim to construct an initial basis that is sparse and will reduce
the fill-in and computational effort during LU factorization and updates that
are utilized in m...
Improving branch-and-cut performance by random sampling
Mathematical Programming Computation - Tập 8 - Trang 113-132 - 2015
We discuss the variability in the performance of multiple runs of branch-and-cut
mixed integer linear programming solvers, and we concentrate on the one deriving
from the use of different optimal bases of the linear programming relaxations.
We propose a new algorithm exploiting more than one of those bases and we show
that different versions of the algorithm can be used to stabilize and improve
th...
A rotation-based branch-and-price approach for the nurse scheduling problem
Mathematical Programming Computation - - 2020
Maximum-weight stable sets and safe lower bounds for graph coloring
Mathematical Programming Computation - - 2012
acados—a modular open-source framework for fast embedded optimal control
Mathematical Programming Computation - Tập 14 - Trang 147-183 - 2021
This paper presents the acados software package, a collection of solvers for
fast embedded optimization intended for fast embedded applications. Its
interfaces to higher-level languages make it useful for quickly designing an
optimization-based control algorithm by putting together different algorithmic
components that can be readily connected and interchanged. Since the core of
acados is written ...
Minimizing the sum of many rational functions
Mathematical Programming Computation - Tập 8 - Trang 83-111 - 2015
We consider the problem of globally minimizing the sum of many rational
functions over a given compact semialgebraic set. The number of terms can be
large (10 to 100), the degree of each term should be small (up to 10), and the
number of variables can be relatively large (10 to 100) provided some kind of
sparsity is present. We describe a formulation of the rational optimization
problem as a gener...
Exact methods for discrete $${\varGamma }$$-robust interdiction problems with an application to the bilevel knapsack problem
Mathematical Programming Computation - Tập 15 Số 4 - Trang 733-782 - 2023
AbstractDeveloping solution methods for discrete bilevel problems is known to be
a challenging task—even if all parameters of the problem are exactly known. Many
real-world applications of bilevel optimization, however, involve data
uncertainty. We study discrete min-max problems with a follower who faces
uncertainties regarding the parameters of the lower-level problem. Adopting a
$$\varGamma $$ ...
Globally solving nonconvex quadratic programming problems with box constraints via integer programming methods
Mathematical Programming Computation - Tập 10 - Trang 333-382 - 2018
We present effective linear programming based computational techniques for
solving nonconvex quadratic programs with box constraints (BoxQP). We first
observe that known cutting planes obtained from the Boolean Quadric Polytope
(BQP) are computationally effective at reducing the optimality gap of BoxQP. We
next show that the Chvátal–Gomory closure of the BQP is given by the odd-cycle
inequalities ...
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