M. Delfour and J.-P. Zolesio. Intrinsic differential geometry and theory of thin shells. Quaderni, Scuola Normale Superiore (Pisa, Italy), to appear, 2000. Home/Search Document Not in Database Summary Related Articles Check |
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A New Differential Formalism for Optimization of Set Functions - Nguyen, Kreinovich (1997) (Correct)
....surface. For this case, useful differential formalisms have been developed. These formalisms use the fact that small (smooth) deviations from the optimal shape cannot increase the value of the objective function to deduce partial differential equations that describe the optimal shapes; see, e.g. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 39, 40, 41, 42, 43, 44, 57]. These papers use different approaches to translate set optimization into function optimization: e.g. one possibility it to replace a set a by a function d(x; a) that describes the distance from each point x to this set; a more appropriate approach [7] is to use the oriented distance, i.e. ....
M. C. Delfour and J.-P. Zolesio, Intrinsic differential geometry and theory of thin shells, Scuola Normale di Pisa, to appear.
How to Divide a Territory? A New Simple Differential.. - Nguyen, Kreinovich (1999) (Correct)
....Their Successes (In Brief) and Territorial Division Problem as a Challenge 2.1 The Existing Methods of Optimizing Set Functions: A Brief Mention The existing methods. There exist many useful differential formalisms for optimizing set functions; an interested reader is referred, e.g. to [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 44, 45, 46, 47, 48, 49, 64] (this is, of course, not an exhaustive list, set function differentiation is a widely developed area) Some of these methods are mainly oriented towards the the case when the optimized set has some smoothness, i.e. in practical terms, when we are optimizing a shape that is described by a smooth ....
M. C. Delfour and J.-P. Zolesio, Intrinsic differential geometry and theory of thin shells, Scuola Normale di Pisa, to appear.
How To Deal with Point Correspondences and.. - Pons, Hermosillo.. (2003) (2 citations) (Correct)
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M. Delfour and J.-P. Zolesio. Intrinsic differential geometry and theory of thin shells. Quaderni, Scuola Normale Superiore (Pisa, Italy), to appear, 2000.
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