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  • 1
    Publication Date: 2019-06-28
    Description: We present a convergence theory for pattern search methods for solving bound constrained nonlinear programs. The analysis relies on the abstract structure of pattern search methods and an understanding of how the pattern interacts with the bound constraints. This analysis makes it possible to develop pattern search methods for bound constrained problems while only slightly restricting the flexibility present in pattern search methods for unconstrained problems. We prove global convergence despite the fact that pattern search methods do not have explicit information concerning the gradient and its projection onto the feasible region and consequently are unable to enforce explicitly a notion of sufficient feasible decrease.
    Keywords: Numerical Analysis
    Type: NASA-CR-198306 , NAS 1.26:198306 , ICASE-96-20
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  • 2
    Publication Date: 2019-06-28
    Description: We extend pattern search methods to linearly constrained minimization. We develop a general class of feasible point pattern search algorithms and prove global convergence to a Karush-Kuhn-Tucker point. As in the case of unconstrained minimization, pattern search methods for linearly constrained problems accomplish this without explicit recourse to the gradient or the directional derivative. Key to the analysis of the algorithms is the way in which the local search patterns conform to the geometry of the boundary of the feasible region.
    Keywords: Numerical Analysis
    Type: NASA/CR-1998-206904 , NAS 1.26:206904 , ICASE-98-3
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  • 3
    Publication Date: 2019-06-28
    Description: This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.
    Keywords: Numerical Analysis
    Type: NASA-CR-201659 , NAS 1.26:201659 , ICASE-97-12 , SIAM Review
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  • 4
    Publication Date: 2019-07-13
    Description: We discuss criteria by which one can classify, analyze, and evaluate approaches to solving multidisciplinary design optimization (MDO) problems. Central to our discussion is the often overlooked distinction between questions of formulating MDO problems and solving the resulting computational problem. We illustrate our general remarks by comparing several approaches to MDO that have been proposed.
    Keywords: Aircraft Design, Testing and Performance
    Type: First ASMO UK/ISSMO CONFERENCE on Engineering Design Optimization; Jul 08, 1999 - Jul 09, 1999; Unknown
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  • 5
    Publication Date: 2019-07-13
    Description: Approximation/model management optimization (AMMO) is a rigorous methodology for attaining solutions of high-fidelity optimization problems with minimal expense in high- fidelity function and derivative evaluation. First-order AMMO frameworks allow for a wide variety of models and underlying optimization algorithms. Recent demonstrations with aerodynamic optimization achieved three-fold savings in terms of high- fidelity function and derivative evaluation in the case of variable-resolution models and five-fold savings in the case of variable-fidelity physics models. The savings are problem dependent but certain trends are beginning to emerge. We give an overview of the first-order frameworks, current computational results, and an idea of the scope of the first-order framework applicability.
    Keywords: Administration and Management
    Type: 1st International Workshop on Surrogate Modelling and Space Mapping for Engineering Opt.; Nov 16, 2000 - Nov 19, 2000; Denmark
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  • 6
    Publication Date: 2019-07-13
    Description: This paper discusses certain connections between nonlinear programming algorithms and the formulation of optimization problems for systems governed by state constraints. The major points of this paper are the detailed calculation of the sensitivities associated with different formulations of optimization problems and the identification of some useful relationships between different formulations. These relationships have practical consequences; if one uses a reduced basis nonlinear programming algorithm, then the implementations for the different formulations need only differ in a single step.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-198234 , NAS 1.26:198234 , ICASE-95-76 , NIPS-96-07992 , Proceedings of the ICASE/LaRC Workshop on Multidisciplinary Design Optimization; Jan 01, 1996; United States
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  • 7
    Publication Date: 2019-08-13
    Description: This work is concerned with an approach to formulating the multidisciplinary optimization (MDO) problem that reflects an algorithmic perspective on MDO problem solution. The algorithmic perspective focuses on formulating the problem in light of the abilities and inabilities of optimization algorithms, so that the resulting nonlinear programming problem can be solved reliably and efficiently by conventional optimization techniques. We propose a modular approach to formulating MDO problems that takes advantage of the problem structure, maximizes the autonomy of implementation, and allows for multiple easily interchangeable problem statements to be used depending on the available resources and the characteristics of the application problem.
    Keywords: Computer Programming and Software
    Type: AIAA Paper 2000-4719 , Multidisciplinary Analysis and Optimization; Sep 06, 2000 - Sep 08, 2000; Long Beach, CA; United States
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  • 8
    Publication Date: 2019-08-13
    Description: Historical evolution of engineering disciplines and the complexity of the MDO problem suggest that disciplinary autonomy is a desirable goal in formulating and solving MDO problems. We examine the notion of disciplinary autonomy and discuss the analytical properties of three approaches to formulating and solving MDO problems that achieve varying degrees of autonomy by distributing the problem along disciplinary lines. Two of the approaches-Optimization by Linear Decomposition and Collaborative Optimization-are based on bi-level optimization and reflect what we call a structural perspective. The third approach, Distributed Analysis Optimization, is a single-level approach that arises from what we call an algorithmic perspective. The main conclusion of the paper is that disciplinary autonomy may come at a price: in the bi-level approaches, the system-level constraints introduced to relax the interdisciplinary coupling and enable disciplinary autonomy can cause analytical and computational difficulties for optimization algorithms. The single-level alternative we discuss affords a more limited degree of autonomy than that of the bi-level approaches, but without the computational difficulties of the bi-level methods. Key Words: Autonomy, bi-level optimization, distributed optimization, multidisciplinary optimization, multilevel optimization, nonlinear programming, problem integration, system synthesis
    Keywords: Computer Programming and Software
    Type: AIAA Paper 2000-4718 , Multidisciplinary Analysis and Optimization; Sep 06, 2000 - Sep 08, 2000; Long Beach, CA; United States
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  • 9
    Publication Date: 2019-07-13
    Description: We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.
    Keywords: Numerical Analysis
    Type: NASA-CR-206247 , NAS 1.26:206247 , ICASE-97-61 , AFOSR Workshop on Optimal Design; Jan 01, 1997; Arlington, VA; United States
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  • 10
    Publication Date: 2019-07-13
    Description: Integrating autonomous disciplines into a problem amenable to solution presents a major challenge in realistic multidisciplinary design optimization (MDO). We propose a linguistic approach to MDO problem description, formulation, and solution we call reconfigurable multidisciplinary synthesis (REMS). With assistance from computer science techniques, REMS comprises an abstract language and a collection of processes that provide a means for dynamic reasoning about MDO problems in a range of contexts. The approach may be summarized as follows. Description of disciplinary data according to the rules of a grammar, followed by lexical analysis and compilation, yields basic computational components that can be assembled into various MDO problem formulations and solution algorithms, including hybrid strategies, with relative ease. The ability to re-use the computational components is due to the special structure of the MDO problem. The range of contexts for reasoning about MDO spans tasks from error checking and derivative computation to formulation and reformulation of optimization problem statements. In highly structured contexts, reconfigurability can mean a straightforward transformation among problem formulations with a single operation. We hope that REMS will enable experimentation with a variety of problem formulations in research environments, assist in the assembly of MDO test problems, and serve as a pre-processor in computational frameworks in production environments. Part 1 of two companion papers, discusses the fundamentals of REMS. This paper, Part 2 illustrates the methodology in more detail.
    Keywords: Systems Analysis and Operations Research
    Type: AIAA Paper 2004-4308-Pt-2 , 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference; Aug 30, 2004 - Sep 01, 2004; Albany, NY; United States
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