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Publication# Accelerated and adaptive modifier-adaptation schemes for the real-time optimization of uncertain systems

Abstract

The steady-state performance of a parametrically or structurally uncertain system can be optimized using iterative real-time optimization methods such as modifier adaptation. Here, we extend a recently proposed second-order modifier-adaptation scheme in two important directions. First, we accelerate its convergence, that is, we reduce the number of potentially time-consuming and suboptimal transitions to intermediate steady states by appropriate filtering. Second, we propose an adaptation strategy to reduce conservatism and prevent divergence that could arise from the unknown curvature of the steady-state system performance. Moreover, we combine these two innovations in the unconstrained and convex case and propose a modified acceleration mechanism for constrained and nonconvex problems. Finally, we demonstrate the benefits on two numerical examples. (C) 2018 Elsevier Ltd. All rights reserved.

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Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

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Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of the function . Given a possibly nonlinear and non-convex continuous function with the global minima and the set of all global minimizers in , the standard minimization problem can be given as that is, finding and a global minimizer in ; where is a (not necessarily convex) compact set defined by inequalities .

Convex optimization

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.

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