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SUMMARY:Isaac Brugge (UFV)
DTSTART:20261103T000000Z
DTEND:20261103T010000Z
DTSTAMP:20261109T050834Z
UID:UFV-math-stats/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UFV-math-sta
 ts/41/">Bellman Functions: A Toy Problem</a>\nby Isaac Brugge (UFV) as par
 t of Fraser Valley Math & Stats Seminar\n\nLecture held in A-252.\n\nAbstr
 act\nSuppose we have two functions $f_1\,f_2$ defined on an interval\n$I$ 
 that have their respective bounds $a_i \\leq f_i \\leq b_i$\nand averages 
 $\\langle f_i \\rangle_I = x_i$\, and we want to see\nhow small or large t
 heir scalar product can be.\nThis means we are interested in the following
  optimization\nproblems:\n\\[\n\\mathbb{B}^{\\max} \\overset{\\mathrm{def}
 }{=}\n\\sup\\left\\{\n\\langle f_1 f_2 \\rangle_I :\na_i \\leq f_i \\leq b
 _i\,\\\;\n\\langle f_i \\rangle_I = x_i\n\\right\\}\,\n\\]\n\\[\n\\mathbb{
 B}^{\\min} \\overset{\\mathrm{def}}{=}\n\\inf\\left\\{\n\\langle f_1 f_2 \
 \rangle_I :\na_i \\leq f_i \\leq b_i\,\\\;\n\\langle f_i \\rangle_I = x_i\
 n\\right\\}.\n\\]\n\nThis is one of the simplest problems regarding Bellma
 n\nfunctions that nevertheless helps to get some understanding\nof their t
 heory.\n
LOCATION:https://researchseminars.org/talk/UFV-math-stats/41/
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