arXiv subjects

Gene A. Bunin

Publications and source records attributed to Gene A. Bunin.

10 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.

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arXiv2016

Constraint back-offs for safe, sufficient excitation: a general theory with application to experimental optimization

In many experimental settings, one is tasked with obtaining information about certain relationships by applying perturbations to a set of independent variables and noting the changes in the set of dependent ones. While traditional design-of-experiments methods are often well-suited for this, the task becomes significantly more difficult in the presence of constraints, which may make it impossible to sufficiently excite the experimental system without incurring constraint violations. The key contribution of this paper consists in deriving constraint back-off sizes sufficient to guarantee that one can always perturb in a ball of radius $δ_e$ without leaving the constrained space, with $δ_e$ set by the user. Additionally, this result is exploited in the context of experimental optimization to propose a constrained version of G. E. P. Box's evolutionary operation technique. The proposed algorithm is applied to three case studies and is shown to consistently converge to the neighborhood of the optimum without violating constraints.

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arXiv2015

Extended reverse-convex programming: an approximate enumeration approach to global optimization

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many branch-and-bound methods, the proposed approach approximates the NLP problem by a reverse-convex programming (RCP) problem to a controlled precision, with the latter then solved by an enumerative search. To establish the theoretical guarantees of the method, the notion of "RCP regularity" is introduced and it is proven that enumeration is guaranteed to yield a global optimum when the RCP problem is regular. An extended RCP algorithmic framework is then presented and its performance is examined for a small set of test problems.

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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.

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arXiv2014

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 a simplification of the latter when the problem is unconstrained. This relation is then exploited to propose a globally convergent modifier-adaptation algorithm using already developed trust-region theory. Cases when the two may not be equivalent and extensions to constrained problems are also discussed.

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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.

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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.

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arXiv2014

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.

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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.

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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.

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