       Re: Minimize with complex values

• To: mathgroup at smc.vnet.net
• Subject: [mg91480] Re: [mg91462] Minimize with complex values
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sat, 23 Aug 2008 01:42:14 -0400 (EDT)
• References: <200808220714.DAA18613@smc.vnet.net>

```shama shahbaz wrote:
> HI
> i want to minimize the absolute value of the following expression  how ca=
> n i do this in methamatica

I assume you mean "Mathematica".

> [exp(pi/4) +exp(3*pi/4)*exp(jp)]+[exp(pi/4) *exp(-5*pi*/4)]+[exp(3*pi/4=
> )*exp(-3*pi*j/4)exp(jp)]+
>
> [exp(pi/4) *exp(-10*pi*j/4)]+[exp(pi/4) *exp(-3*pi*j/2)exp(jp)]+[exp(pi=
> /4)*exp(-15*pi*j/4)]+
>
> [exp(3*pi/4)*exp(-9*pi*j/4)exp(jp)]
>
> p is the unknown value ,and it represent the phase...which is other than 0 =
> .....is there any way to calculate it.
> Regards

One way would be to write the objective function in viable Mathematica
syntax, then use an optimization function such as NMinimize.

expression = Abs[Exp[Pi/4] + Exp[3*Pi/4]*Exp[I*p] +
Exp[Pi/4]*Exp[-5*Pi*I/4] + Exp[3*Pi/4]*Exp[-3*Pi*I/4]*Exp[I*p] +
Exp[Pi/4]*Exp[-10*Pi*I/4] + Exp[Pi/4]*Exp[-3*Pi*I/2]*Exp[I*p] +
Exp[Pi/4]*Exp[-15*Pi*I/4] + Exp[3*Pi/4]*Exp[-9*Pi*I/4]Exp[I*p]];

In:= NMinimize[expression, p]
Out= {14.1582, {p -> -1.87025}}

Generally speaking, if you want to use Mathematica on a problem, you
will need to use Mathematica syntax and Mathematica functions.

Daniel Lichtblau
Wolfram Research

```

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