Abstract
This paper deals with optimization of constrained functionals with distributed parameters. The functionals may be chosen for identifying parameters that optimize performance or minimize energy forms, or for computation of eigenvalues via the Rayleigh quotient. Constraints may represent design limitations, extremes of operating conditions, or state equations for dynamical systems. The intrinsic nature of iterative solution methods for functional minimization, the functional sensitivity analysis, and state function sensitivity analysis have been the subject of extensive research. Using simple examples from engineering, this paper points out some pitfalls for gradient-type computational methods particularly in connection with computing of unstable processes or eigenvalues via minimization of a constrained Rayleigh quotient. Auxiliary conditions involving energy levels of the system for constrained problems are suggested as indicators of existence of multiple gradient directions.
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Komkov, V., Irwin, C. (1984). Uniqueness for gradient methods in engineering optimization. In: Komkov, V. (eds) Sensitivity of Functionals with Applications to Engineering Sciences. Lecture Notes in Mathematics, vol 1086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073071
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DOI: https://doi.org/10.1007/BFb0073071
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