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Ee364a homework 6 solutions

What is the solution of the norm approximation problem with one scalar variable x R , minimize b x 1 b b , for the 1-, 2-, and -norms? (c) -norm: the midrange point (max b i min b i ) / 2. Show that the following problem is quasiconvex: minimize max i =1 ,...,k v v v v v p ( t i ) q ( t i ) y i v v v v v where p ( t ) = a a 1 t a 2 t 2 a m t m , q ( t ) = 1 b 1 t b n t n , and the domain of the objective function is dened as D = . In this problem we t a rational function p ( t ) /q ( t ) to given data, while constraining the denominator polynomial to be positive on the interval [ , ]. All homework is due by 5 pm in the inbox across the hall from Packard 243. All numbered exercises are from the textbook; exercises which start with ‘A’ are from the set of additional exercises posted on the textbook website.

Ee364a homework 6 solutions

Ee364a homework 6 solutions

The interpolation points t i [ , ], and desired function values y i , i = 1 , . In addition, most students have access to systems located in their research areas.

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  • 1 2 3 Could f be convex (concave, quasiconvex, quasiconcave)? 1 1 2 3 I II Along this line the function passes through the points marked as black dots in the Fgure below.


    Ee364a homework 6 solutions

    Ee364a homework 6 solutions

    Ee364a homework 6 solutions

    Let x be any point in H , so by our assumption, x is also in H , i.e. We have a T ( x tv ) = a T x b for all t R , so x tv H for all t R . However, a T ( x tv ) = a T x t a T v , and since a T v n = 0, we will have a T ( x tv ) > b for suciently large t > 0 or suciently small t < 0. However for t large enough we will have a T ( x ta ) = a T x t b a b 2 2 > b , so x ta n H . inally, we assume a = a for some > 0 but b < b . The Department of Computer Science (CS) operates and supports computing facilities for departmental education, research, and administration needs.

    Ee364a homework 6 solutions

    Servers and workstations running Linux or various versions of Windows are commonplace. HOW NOT TO WRITE A PAPER All CS students have access to the departmental student machine for general use (mail, news, etc.), as well as computer labs with public workstations located in the Gates Building.


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