52,484 research outputs found
Recent contributions to linear semi-infinite optimization
This paper reviews the state-of-the-art in the theory of deterministic and uncertain linear semi-infinite optimization, presents some numerical approaches to this type of problems, and describes a selection of recent applications in a variety of fields. Extensions to related optimization areas, as convex semi-infinite optimization, linear infinite optimization, and multi-objective linear semi-infinite optimization, are also commented.This work was supported by the MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P, and by the Australian Research Council, Project DP160100854
Recent contributions to linear semi-infinite optimization: an update
This paper reviews the state-of-the-art in the theory of deterministic and uncertain linear semi-infinite optimization, presents some numerical approaches to this type of problems, and describes a selection of recent applications in a variety of fields. Extensions to related optimization areas, as convex semi-infinite optimization, linear infinite optimization, and multi-objective linear semi-infinite optimization, are also commented.This is an updated version of the paper “Recent contributions to linear semi-infinite optimization” that appeared in 4OR, 15(3), 221–264 (2017). It was supported by the MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P, and by the Australian Research Council, Project DP160100854
Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
In a recent series of papers, Gebremariam, Bogner, and Duguet derived a
microscopically based nuclear energy density functional by applying the Density
Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral
effective field theory (EFT) two- and three-nucleon interactions. Due to the
structure of the chiral interactions, each coupling in the DME functional is
given as the sum of a coupling constant arising from zero-range contact
interactions and a coupling function of the density arising from the
finite-range pion exchanges. Since the contact contributions have essentially
the same structure as those entering empirical Skyrme functionals, a
microscopically guided Skyrme phenomenology has been suggested in which the
contact terms in the DME functional are released for optimization to
finite-density observables to capture short-range correlation energy
contributions from beyond Hartree-Fock. The present paper is the first attempt
to assess the ability of the newly suggested DME functional, which has a much
richer set of density dependencies than traditional Skyrme functionals, to
generate sensible and stable results for nuclear applications. The results of
the first proof-of-principle calculations are given, and numerous practical
issues related to the implementation of the new functional in existing Skyrme
codes are discussed. Using a restricted singular value decomposition (SVD)
optimization procedure, it is found that the new DME functional gives
numerically stable results and exhibits a small but systematic reduction of our
test function compared to standard Skyrme functionals, thus justifying
its suitability for future global optimizations and large-scale calculations.Comment: 17 pages, 6 figure
From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming
We consider linear programming (LP) problems in infinite dimensional spaces
that are in general computationally intractable. Under suitable assumptions, we
develop an approximation bridge from the infinite-dimensional LP to tractable
finite convex programs in which the performance of the approximation is
quantified explicitly. To this end, we adopt the recent developments in two
areas of randomized optimization and first order methods, leading to a priori
as well as a posterior performance guarantees. We illustrate the generality and
implications of our theoretical results in the special case of the long-run
average cost and discounted cost optimal control problems for Markov decision
processes on Borel spaces. The applicability of the theoretical results is
demonstrated through a constrained linear quadratic optimal control problem and
a fisheries management problem.Comment: 30 pages, 5 figure
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