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Chapter and Conference Paper
Piecewise Polynomial Taylor Expansions—The Generalization of Faà di Bruno’s Formula
We present an extension of Taylor’s Theorem for the piecewise polynomial expansion of non-smooth evaluation procedures involving absolute value operations. Evaluation procedures are computer programs of mathem...
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Chapter
Beyond the Oracle: Opportunities of Piecewise Differentiation
For more than 30 years much of the research and development in nonsmooth optimization has been predicated on the assumption that the user provides an oracle that evaluates at any given x ∈ ℝ n $${\bol...
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Article
An algorithm for nonsmooth optimization by successive piecewise linearization
We present an optimization method for Lipschitz continuous, piecewise smooth (PS) objective functions based on successive piecewise linearization. Since, in many realistic cases, nondifferentiabilities are cau...
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Chapter and Conference Paper
Treating Artificial Neural Net Training as a Nonsmooth Global Optimization Problem
We attack the classical neural network training problem by successive piecewise linearization, applying three different methods for the global optimization of the local piecewise linear models. The methods are...
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Article
On Lipschitz optimization based on gray-box piecewise linearization
We address the problem of minimizing objectives from the class of piecewise differentiable functions whose nonsmoothness can be encapsulated in the absolute value function. They possess local piecewise linear ...
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Article
Adaptive sequencing of primal, dual, and design steps in simulation based optimization
Many researchers have used Oneshot optimization methods based on user-specified primal state iterations, the corresponding adjoint iterations, and appropriately preconditioned design steps. Our goal here is to...
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Book
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Chapter
Introduction to Part V: Applications
In this part a variety of important applications in the field of PDE constrained optimization and optimal control is presented. The results range from physical and chemical over electronic to biomedical and -t...
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Chapter
Introduction to Part I Constrained Optimization, Identification and Control
In the article Optimal Control of Allen-Cahn Systems the authors Luise Blank, M. Hassan Farshbaf-Shaker, Claudia Hecht, Josef Michl and Christoph Rupprecht report results of their project regarding a control prob...
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Chapter
Introduction
Problems of optimization and optimal control subject to constraints governed by partial differential equations (PDEs) arise in a huge variety of industrial, technological, economic, medical and environmental a...
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Chapter
One-Shot Approaches to Design Optimzation
The paper describes general methodologies for the solution of design optimization problems. In particular we outline the close relations between a fixed point solver based piggy back approach and a Reduced SQP...
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Chapter and Conference Paper
Representation and Analysis of Piecewise Linear Functions in Abs-Normal Form
It follows from the well known min/max representation given by Scholtes in his recent Springer book, that all piecewise linear continuous functions ...
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Chapter
Optimal Design with Bounded Retardation for Problems with Non-separable Adjoints
In the natural and enginiering sciences numerous sophisticated simulation models involving PDEs have been developed. In our research we focus on the transition from such simulation codes to optimization, where...
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Article
A method for pointwise evaluation of polyconvex envelopes
We investigate a method for computing the value of a polyconvex envelope at a given feed \({A^0 \in \mathbb{R}^{m \times n}}\) ...
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Chapter and Conference Paper
From the Product Example to PDE Adjoints, Algorithmic Differentiation and Its Application (Invited Talk)
At the last conference on algorithmic or automatic differentiation (AD) in July 2012, Bert Speelpenning gave a very entertaining account of his pioneering work in the field. After finishing his thesis titled Comp...
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Chapter
Quantifying Retardation in Simulation Based Optimization
In many applications one wishes to optimize designs on the basis of an established simulation tool. We consider the situation where “simulation” means solving a system of state equations by a fixed point itera...
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Article
On the numerical stability of algorithmic differentiation
In contrast to integration, the differentiation of a function is an ill-conditioned process, if only an oracle is available for its pointwise evaluation. That is, unrelated small variations in the value of the co...
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Book
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Chapter and Conference Paper
The Relative Cost of Function and Derivative Evaluations in the CUTEr Test Set
The CUTEr test set represents a testing environment for nonlinear optimization solvers containing more than 1,000 academic and applied nonlinear problems. It is often used to verify the robustness and performa...
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Chapter
Automated Extension of Fixed Point PDE Solvers for Optimal Design with Bounded Retardation
We study PDE-constrained optimization problems where the state equation is solved by a pseudo-time step** or fixed point iteration. We present a technique that improves primal, dual feasibility and optimalit...
