273 research outputs found
Objective acceleration for unconstrained optimization
Acceleration schemes can dramatically improve existing optimization
procedures. In most of the work on these schemes, such as nonlinear Generalized
Minimal Residual (N-GMRES), acceleration is based on minimizing the
norm of some target on subspaces of . There are many numerical
examples that show how accelerating general purpose and domain-specific
optimizers with N-GMRES results in large improvements. We propose a natural
modification to N-GMRES, which significantly improves the performance in a
testing environment originally used to advocate N-GMRES. Our proposed approach,
which we refer to as O-ACCEL (Objective Acceleration), is novel in that it
minimizes an approximation to the \emph{objective function} on subspaces of
. We prove that O-ACCEL reduces to the Full Orthogonalization
Method for linear systems when the objective is quadratic, which differentiates
our proposed approach from existing acceleration methods. Comparisons with
L-BFGS and N-CG indicate the competitiveness of O-ACCEL. As it can be combined
with domain-specific optimizers, it may also be beneficial in areas where
L-BFGS or N-CG are not suitable.Comment: 18 pages, 6 figures, 5 table
A parametric level-set method for partially discrete tomography
This paper introduces a parametric level-set method for tomographic
reconstruction of partially discrete images. Such images consist of a
continuously varying background and an anomaly with a constant (known)
grey-value. We represent the geometry of the anomaly using a level-set
function, which we represent using radial basis functions. We pose the
reconstruction problem as a bi-level optimization problem in terms of the
background and coefficients for the level-set function. To constrain the
background reconstruction we impose smoothness through Tikhonov regularization.
The bi-level optimization problem is solved in an alternating fashion; in each
iteration we first reconstruct the background and consequently update the
level-set function. We test our method on numerical phantoms and show that we
can successfully reconstruct the geometry of the anomaly, even from limited
data. On these phantoms, our method outperforms Total Variation reconstruction,
DART and P-DART.Comment: Paper submitted to 20th International Conference on Discrete Geometry
for Computer Imager
Gnowee: A Hybrid Metaheuristic Optimization Algorithm for Constrained, Black Box, Combinatorial Mixed-Integer Design
This paper introduces Gnowee, a modular, Python-based, open-source hybrid
metaheuristic optimization algorithm (Available from
https://github.com/SlaybaughLab/Gnowee). Gnowee is designed for rapid
convergence to nearly globally optimum solutions for complex, constrained
nuclear engineering problems with mixed-integer and combinatorial design
vectors and high-cost, noisy, discontinuous, black box objective function
evaluations. Gnowee's hybrid metaheuristic framework is a new combination of a
set of diverse, robust heuristics that appropriately balance diversification
and intensification strategies across a wide range of optimization problems.
This novel algorithm was specifically developed to optimize complex nuclear
design problems; the motivating research problem was the design of material
stack-ups to modify neutron energy spectra to specific targeted spectra for
applications in nuclear medicine, technical nuclear forensics, nuclear physics,
etc. However, there are a wider range of potential applications for this
algorithm both within the nuclear community and beyond. To demonstrate Gnowee's
behavior for a variety of problem types, comparisons between Gnowee and several
well-established metaheuristic algorithms are made for a set of eighteen
continuous, mixed-integer, and combinatorial benchmarks. These results
demonstrate Gnoweee to have superior flexibility and convergence
characteristics over a wide range of design spaces. We anticipate this wide
range of applicability will make this algorithm desirable for many complex
engineering applications.Comment: 43 pages, 7 tables, 6 figure
Projection-Based and Look Ahead Strategies for Atom Selection
In this paper, we improve iterative greedy search algorithms in which atoms
are selected serially over iterations, i.e., one-by-one over iterations. For
serial atom selection, we devise two new schemes to select an atom from a set
of potential atoms in each iteration. The two new schemes lead to two new
algorithms. For both the algorithms, in each iteration, the set of potential
atoms is found using a standard matched filter. In case of the first scheme, we
propose an orthogonal projection strategy that selects an atom from the set of
potential atoms. Then, for the second scheme, we propose a look ahead strategy
such that the selection of an atom in the current iteration has an effect on
the future iterations. The use of look ahead strategy requires a higher
computational resource. To achieve a trade-off between performance and
complexity, we use the two new schemes in cascade and develop a third new
algorithm. Through experimental evaluations, we compare the proposed algorithms
with existing greedy search and convex relaxation algorithms.Comment: sparsity, compressive sensing; IEEE Trans on Signal Processing 201
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