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 Ti3+^{3 +} 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