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

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.

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

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.

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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