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Finance Notes_Part_25

# Finance Notes_Part_25 - Limitations of gps c c Audet and...

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Unformatted text preview: Limitations of gps c c Audet and Vicente (SIOPT 2008) c u c c u c c u c c Optimization under general constraints c u c c 70/109 Limitations of gps cc ccc uu c ccccc u c c Audet and Vicente (SIOPT 2008) Optimization under general constraints c u c c 70/109 Limitations of gps T ccc cccu uu c ' c c c c c Ec u c c c c For almost all starting points, the iterates of gps with the coordinate directions converge to a point x on the diagonal, where f is not ˆ diﬀerentiable, with f (x; ±ei ) ≥ 0 ˆ but f (x; d) < 0 with d = (1, −1)T . ˆ Audet and Vicente (SIOPT 2008) Optimization under general constraints 70/109 Limitations of gps - a convex problem Minimize f (x) = x1 + x2 on a disc ................... ....................... ........ ..... ....... ..... ..... .... ..... .... .... ... .... .. .. ... .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. .. .. ... .. ... .... ... .... .... ..... .... ..... ..... ....... .......... .............. ....................... ...... T Audet and Vicente (SIOPT 2008) E Optimization under general constraints 71/109 Limitations of gps - a convex problem Minimize f (x) = x1 + x2 on a disc ................... ....................... ........ ..... ....... ..... ..... .... ..... .... .... ... .... .. .. ... .. .. .. .. .. .. .. . .. .. .. .. .. . .. .. .. .. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . .. .. .. . .. .. .. .. .. .. .. .. . .. .. .. .. .. .. ... .. ... .... ... .... .... ..... .... ..... ..... ....... .......... .............. ....................... ...... T u Audet and Vicente (SIOPT 2008) E Optimization under general constraints 71/109 ...
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