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

On the equivalence between the modifier-adaptation and trust-region frameworks

In this short note, the recently popular modifier-adaptation framework for real-time optimization is discussed in tandem with the well-developed trust-region framework of numerical optimization, and it is shown that the basic version of the former is simply a special case of the latter. This relation is then exploited to propose a globally convergent modifier-adaptation algorithm using already developed trust-region theory. Cases when the two are not equivalent are also discussed

Implementation techniques for the SCFO experimental optimization framework

The material presented in this document is intended as a comprehensive, implementation-oriented supplement to the experimental optimization framework presented in a companion document. The issues of physical degradation, unknown Lipschitz constants, measurement/estimation noise, gradient estimation, sufficient excitation, and the handling of soft constraints and/or a numerical cost function are all addressed, and a robust, implementable version of the sufficient conditions for feasible-side global convergence is proposed.Comment: supplementary document; 66 page