17,616 research outputs found
On SOCP-based disjunctive cuts for solving a class of integer bilevel nonlinear programs
We study a class of integer bilevel programs with second-order cone
constraints at the upper-level and a convex-quadratic objective function and
linear constraints at the lower-level. We develop disjunctive cuts (DCs) to
separate bilevel-infeasible solutions using a second-order-cone-based
cut-generating procedure. We propose DC separation strategies and consider
several approaches for removing redundant disjunctions and normalization. Using
these DCs, we propose a branch-and-cut algorithm for the problem class we
study, and a cutting-plane method for the problem variant with only binary
variables.
We present an extensive computational study on a diverse set of instances,
including instances with binary and with integer variables, and instances with
a single and with multiple linking constraints. Our computational study
demonstrates that the proposed enhancements of our solution approaches are
effective for improving the performance. Moreover, both of our approaches
outperform a state-of-the-art generic solver for mixed-integer bilevel linear
programs that is able to solve a linearized version of our binary instances.Comment: arXiv admin note: substantial text overlap with arXiv:2111.0682
Reduced Memory Footprint in Multiparametric Quadratic Programming by Exploiting Low Rank Structure
In multiparametric programming an optimization problem which is dependent on
a parameter vector is solved parametrically. In control, multiparametric
quadratic programming (mp-QP) problems have become increasingly important since
the optimization problem arising in Model Predictive Control (MPC) can be cast
as an mp-QP problem, which is referred to as explicit MPC. One of the main
limitations with mp-QP and explicit MPC is the amount of memory required to
store the parametric solution and the critical regions. In this paper, a method
for exploiting low rank structure in the parametric solution of an mp-QP
problem in order to reduce the required memory is introduced. The method is
based on ideas similar to what is done to exploit low rank modifications in
generic QP solvers, but is here applied to mp-QP problems to save memory. The
proposed method has been evaluated experimentally, and for some examples of
relevant problems the relative memory reduction is an order of magnitude
compared to storing the full parametric solution and critical regions
An improved multi-parametric programming algorithm for flux balance analysis of metabolic networks
Flux balance analysis has proven an effective tool for analyzing metabolic
networks. In flux balance analysis, reaction rates and optimal pathways are
ascertained by solving a linear program, in which the growth rate is maximized
subject to mass-balance constraints. A variety of cell functions in response to
environmental stimuli can be quantified using flux balance analysis by
parameterizing the linear program with respect to extracellular conditions.
However, for most large, genome-scale metabolic networks of practical interest,
the resulting parametric problem has multiple and highly degenerate optimal
solutions, which are computationally challenging to handle. An improved
multi-parametric programming algorithm based on active-set methods is
introduced in this paper to overcome these computational difficulties.
Degeneracy and multiplicity are handled, respectively, by introducing
generalized inverses and auxiliary objective functions into the formulation of
the optimality conditions. These improvements are especially effective for
metabolic networks because their stoichiometry matrices are generally sparse;
thus, fast and efficient algorithms from sparse linear algebra can be leveraged
to compute generalized inverses and null-space bases. We illustrate the
application of our algorithm to flux balance analysis of metabolic networks by
studying a reduced metabolic model of Corynebacterium glutamicum and a
genome-scale model of Escherichia coli. We then demonstrate how the critical
regions resulting from these studies can be associated with optimal metabolic
modes and discuss the physical relevance of optimal pathways arising from
various auxiliary objective functions. Achieving more than five-fold
improvement in computational speed over existing multi-parametric programming
tools, the proposed algorithm proves promising in handling genome-scale
metabolic models.Comment: Accepted in J. Optim. Theory Appl. First draft was submitted on
August 4th, 201
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