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Let : IR > IR be a canvex (ontinous uith contont L.' For a hx os follou s. fundion and vf is Lipschitz fixed xE IR", ve define ) Show thot IR". ofh for amy xiyı ElR" t is minimizer Over 2) Show that 3.) any Shou that for 9 Shou that for ony *y E IR" y ty. E IR

Let : IR > IR be a canvex (ontinous uith contont L.' For a hx os follou s. fundion and vf is Lipschitz fixed xE IR", ve define ) Show thot IR". ofh for amy xiyı ElR" t is minimizer Over 2) Show that 3.) any Shou that for 9 Shou that for ony *y E IR" y ty. E IR

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let >IR bea canvex funchion and v continous uith contont L.'For a fixed hx os follou s. is hipschitz xE IR", ve define ) Show that + is minimizer f hx for any *iyı EIR" dver IR" 2) Show that 3.) Shou thot for any foosfy) 9 Shou that for emy ty, E IR"
Transcribed Image Text:Let >IR bea canvex funchion and v continous uith contont L.'For a fixed hx os follou s. is hipschitz xE IR", ve define ) Show that + is minimizer f hx for any *iyı EIR" dver IR" 2) Show that 3.) Shou thot for any foosfy) 9 Shou that for emy ty, E IR"
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