Homework 4 Spring 2014 Solutions - Math 408 Homework Set 4...

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Math 408Homework Set 4 Solutions
(1) Given a point ˆxRnand a directiondRnconsider the functionsφ:RRandψ:RRgiven byφ(t) :=fx+td)andψ(t) :=hx+td),respectively.(a) Show thatφcan be written asφ(t) =α2t2+βt+δand give the values ofα,β, andδ.
(b) Give a necessary and sufficient condition under which the problem mintφ(t) has aglobally optimal solution and give an expression for this solution.

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