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SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
Finite element analysis of nonsmooth contact
, 1999
"... This work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners. Amongst the mathematical tools we bring to bear on the problem is nonsmooth analysis, following Clarke (F.H. Clarke. Optimization and nonsmooth analysis. John Wiley ..."
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Cited by 36 (11 self)
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This work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners. Amongst the mathematical tools we bring to bear on the problem is nonsmooth analysis, following Clarke (F.H. Clarke. Optimization and nonsmooth analysis. John Wiley and Sons, New York, 1983.). We specifically address contact geometries for which both the use of normals and gap functions have difficulties and therefore precludes the application of most contact algorithms proposed to date. Such situations arise in applications such as fragmentation, where angular fragments undergo complex collision sequences before they scatter. We demonstrate the robustness and versatility of the nonsmooth contact algorithms developed in this paper with the aid of selected two and threedimensional applications.
Infeasibility And Negative Curvature In Optimization
, 1999
"... Infeasibility and Negative Curvature in Optimization. Erik G. Boman, Stanford University, 1999. It may seem reasonable that only problems with a solution can be solved. However, in practice it may be that some type of \solution" is needed even when the problem is illposed and no solution exis ..."
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Cited by 5 (0 self)
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Infeasibility and Negative Curvature in Optimization. Erik G. Boman, Stanford University, 1999. It may seem reasonable that only problems with a solution can be solved. However, in practice it may be that some type of \solution" is needed even when the problem is illposed and no solution exists. Our concern is with constrained optimization problems that do not have any feasible points. (We then say the problem is infeasible.) It may be that a small perturbation of some of the constraints would yield a solution, and determining such a perturbation might produce the approximate solution required. However, by allowing a slightly larger pertubation in the constraints, we might nd a much improved value of the objective function. It is quite possible that a \slightly infeasible solution" of this kind would be welcomed by the user. In this thesis we address such issues of infeasibility. Sequential quadratic programming (SQP) methods are a class of methods for solving constrained nonlinear optimization problems. They have been very successful in practice, and are widely regarded as the most ecient direct approach to constrained optimization. As their name suggests, SQP methods are iterative and solve a quadratic program (QP) at each iteration. In convergence analysis it is usually assumed that the QP subproblems always have a feasible point. This assumption is not warranted even when the original nonlinear problem has a feasible point. When the original problem is infeasible, it is almost inevitable that the QP subproblems will be infeasible. One may think this acceptable because if there is no solution to the problem posed, it should not be surprising that an algorithm might break down. However, in practice we would still like a point that in some sense is \good". This the...
CDS and Graduate Aeronautical Laboratories, Caltech
"... This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the early stage of fragmentation when a number of angular fragments undergo complex collision sequences bef ..."
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This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the early stage of fragmentation when a number of angular fragments undergo complex collision sequences before eventually scattering. Such situations precludes the application of most contact algorithms proposed to date. 1 Introduction. The problem of existence and uniqueness in problems involving collisions has a long and distinguished history, going back at least to Painlevé [1895]. In these types of problems, the solutions are not continuous functions of time because of velocity jumps; they are also not continuous with respect to initial conditions. There is no general consensus about the best method for settling this issue; it is clear that the answer
Efficient Computation of Derivatives for Optimal Experimental Design
, 2007
"... Phänomenen stellen in vielen natur und ingenieurwissenschaftlichen Disziplinen ein unverzichtbares Hilfsmittel dar. Dabei ist es oftmals erforderlich, das verwendete Modell mit Hilfe von experimentell gewonnenen Messdaten zu kalibrieren, d.h. so einzustellen, dass die Modellvorhersage bestmöglich m ..."
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Phänomenen stellen in vielen natur und ingenieurwissenschaftlichen Disziplinen ein unverzichtbares Hilfsmittel dar. Dabei ist es oftmals erforderlich, das verwendete Modell mit Hilfe von experimentell gewonnenen Messdaten zu kalibrieren, d.h. so einzustellen, dass die Modellvorhersage bestmöglich mit gegebenen Messdaten aus zuvor durchgeführten physikalischen Experimenten übereinstimmt. Bei der optimalen Versuchsplanung (optimal experimental design) wird versucht, diese Experimente so zu gestalten, dass der Informationsgewinn für die Kalibrierung des Modells maximiert wird. Dazu werden typischerweise mathematische Optimierungsverfahren eingesetzt, wobei zur Berechnung der Zielfunktion die Ableitung des zugrunde liegenden Modells benötigt wird. In dieser Arbeit wird gezeigt, wie man die Modellkalibrierung und optimale Versuchsplanung durch geeignete Software unterstützen kann. Da diese Prozesse oftmals selbst experimentellen Charakter haben, d.h. dass Simulationscode, Optimierungsverfahren und Zielfunktion häufigen Änderungen unterliegen, wird mit EFCOSS eine neue Umgebung zur automatisierten Koppelung der verschiedenen Softwarekomponenten vorgestellt. Insbesondere
Software Supporting Optimal Experimental Design: A Case Study of Binary Diffusion Using EFCOSS
"... Methods for optimal experimental design aim at minimizing uncertainty in parameter estimation problems. Despite their long tradition in applied mathematics and importance in practical applications, they are currently not widely used in computational science and engineering. To make the techniques ..."
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Methods for optimal experimental design aim at minimizing uncertainty in parameter estimation problems. Despite their long tradition in applied mathematics and importance in practical applications, they are currently not widely used in computational science and engineering. To make the techniques of optimal experimental design more accessible to a broader community, we introduce a novel software environment called EFCOSS and demonstrate its ease of use and versatility in two case studies of binary diffusion experiments. Through the use of a componentbased software architecture, integration of automatic differentiation technology and facilitated interfacing to optimization algorithms, EFCOSS minimizes the computational overhead for the user who can thus focus on model development and analysis itself. The presented case studies focus on diffusion experiments in liquids since these experiments are typically very demanding. The use of optimal experimental design techniques allows to reduce experimental time and effort significantly. Key words: optimal experimental design, parameter estimation, EFCOSS,