arXiv subjects

Grégory François

Publications and source records attributed to Grégory François.

6 recordsLinked to original sources

arXiv2017

Lipschitz constants in experimental optimization

The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically oriented applications, but their potential for explicit use in more engineering-based domains has not been explored. The latter point is the subject of this paper, where we propose several ways in which the Lipschitz constants may be used explicitly in the domain of experimental optimization. Specifically, we focus on how they may help ensure the satisfaction of constraints and on their potential role in reducing the negative effects of measurement or estimation uncertainty. A number of refinements to the proposed approaches are also derived, and some techniques for setting the constants are presented.

math.OC↗

arXiv2014

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.

math.OC↗

arXiv2014

On linear and quadratic Lipschitz bounds for twice continuously differentiable functions

Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic bounds that are stated in terms of the Lipschitz constants of the function and the Lipschitz constants of its partial derivatives, and serve to bound the function's evolution over a compact set. While the results follow from basic mathematical principles and are certainly not new, we present them as they are, from our experience, very difficult to find explicitly either in the literature or in most analysis textbooks.

math.OC↗

arXiv2014

Feasible-side global convergence in experimental optimization

We propose a canonical form of the experimental optimization problem and review the state-of-the-art methods to solve it. As guarantees of global convergence to an optimal point via only feasible iterates are absent in these methods, we present a set of sufficient conditions to enforce this behavior.

math.OC↗

arXiv2013

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.

math.OC↗

arXiv2013

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.

math.OC↗