4,033 research outputs found
On the piecewise-concave approximations of functions
The piecewise-concave function may be used to approximate a wide range of
other functions to arbitrary precision over a bounded set. In this short paper,
this property is proven for three function classes: (a) the multivariate twice
continuously differentiable function, (b) the univariate Lipschitz-continuous
function, and (c) the multivariate separable Lipschitz-continuous function.Comment: 4 pages; written as a supplement to submitted journal pape
Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - II. Implementation Issues
The idea of iterative process optimization based on collected output
measurements, or "real-time optimization" (RTO), has gained much prominence in
recent decades, with many RTO algorithms being proposed, researched, and
developed. While the essential goal of these schemes is to drive the process to
its true optimal conditions without violating any safety-critical, or "hard",
constraints, no generalized, unified approach for guaranteeing this behavior
exists. In this two-part paper, we propose an implementable set of conditions
that can enforce these properties for any RTO algorithm. This second part
examines the practical side of the sufficient conditions for feasibility and
optimality (SCFO) proposed in the first and focuses on how they may be enforced
in real application, where much of the knowledge required for the conceptual
SCFO is unavailable. Methods for improving convergence speed are also
considered.Comment: 56 pages, 15 figure
Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - I. Theoretical Foundations
The idea of iterative process optimization based on collected output
measurements, or "real-time optimization" (RTO), has gained much prominence in
recent decades, with many RTO algorithms being proposed, researched, and
developed. While the essential goal of these schemes is to drive the process to
its true optimal conditions without violating any safety-critical, or "hard",
constraints, no generalized, unified approach for guaranteeing this behavior
exists. In this two-part paper, we propose an implementable set of conditions
that can enforce these properties for any RTO algorithm. The first part of the
work is dedicated to the theory behind the sufficient conditions for
feasibility and optimality (SCFO), together with their basic implementation
strategy. RTO algorithms enforcing the SCFO are shown to perform as desired in
several numerical examples - allowing for feasible-side convergence to the
plant optimum where algorithms not enforcing the conditions would fail.Comment: Working paper; supplementary material available at:
http://infoscience.epfl.ch/record/18807
Optimal paths on the road network as directed polymers
We analyze the statistics of the shortest and fastest paths on the road
network between randomly sampled end points. To a good approximation, these
optimal paths are found to be directed in that their lengths (at large scales)
are linearly proportional to the absolute distance between them. This motivates
comparisons to universal features of directed polymers in random media. There
are similarities in scalings of fluctuations in length/time and transverse
wanderings, but also important distinctions in the scaling exponents, likely
due to long-range correlations in geographic and man-made features. At short
scales the optimal paths are not directed due to circuitous excursions governed
by a fat-tailed (power-law) probability distribution.Comment: 5 pages, 7 figure
Comment on ``Conduction states in oxide perovskites: Three manifestations of Ti Jahn-Teller polarons in barium titanate''
In this comment to [S. Lenjer, O. F. Schirmer, H. Hesse, and Th. W. Kool,
Phys. Rev. B {\bf 66}, 165106 (2002)] we discuss the electronic structure of
oxygen vacancies in perovskites. First principles computations are in favour of
rather deep levels in these vacancies, and Lenjer et al suggest that the
electrons' interaction energy is negative, but data on electroconductivity are
against.Comment: 2 pages, no figure
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