A complicated non-convex problem

Main Menu

Login Form

Welcome, Guest
Please Login or Register. Lost Password?

Kunena

General discussion

Help!!!

A complicated non-convex problem

(1 viewing) (1) Guest

Page: 12

TOPIC: A complicated non-convex problem

Forum Tools

#6991

Re: A complicated convex problem, how to figure it out 9 Months, 1 Week ago Karma: 0

I'm so sorry, I forgot the function abs, this version is right:

Code:

% input parameters

N = 17;

L = 175;

omega = 0.015;

r = linspace(3, 15, 100);

% constraint

A = spdiags(ones(N - 1, 1)*[-1 1], [0 -1], N - 1, N - 2);

b = [zeros(N - 2, 1); L];

% optimization

cvx_begin

　　variable x(N - 2);

　　xn = [0; x; L];

　　minimize( max( abs(sum(exp(1i*omega*xn*r), 1)) ) )

　　subject to

　　　　A * x <= b

cvx_end

I mean whether we can get the approximate upper envelope of the function abs(sum(exp(1i*omega*xn*r), 1)), then get max of envelope to find an interesting point.

xdkd1612

Fresh Boarder

Posts: 4

The administrator has disabled public write access.

#6992

Re: A complicated convex problem, how to figure it out 9 Months, 1 Week ago

Karma: 32

Well, when you start computing the envelope etc, you are essentially reinventing a global solver. That is what is performed in the first iteration. After that, the feasible space is partitioned, and envelopes (or approximations of) over the new regions are computed. In every region an LP relaxation is solvers, and a local nonlinear solve, in order to get lower and upper bounds. The information obtained from the first iteration is very bad, as the lower bound on the objective is 0.

users.isy.liu.se/johanl/yalmip/pmwiki.ph...Solvers.BMIBNBTheory

Your new objective would be modeled with
magnitudes = s1.^2+s2.^2 ;
Constraints = [sqrtm(magnitudes) <= t, diff(xn)>=0,s1 == sum(cos(omega*xn*r),1),s2 == sum(sin(omega*xn*r),1)];

BTW, in case you wonder, I am avoiding the use of the max operator (and thus do it manually through t), since it is would fail a convexity propagation (max of sqrt of trigonometric is not structurally convex). Same thing with norm. sqrtm does not perform convexity propagation
users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Extra.SQRT

lofberg

Platinum Boarder

Posts: 2280

Last Edit: 2012/08/14 03:54 By lofberg.

The administrator has disabled public write access.

#6993

Re: A complicated convex problem, how to figure it out 9 Months, 1 Week ago Karma: 32

FYI, the functions looks horrible already in 2D

Code:



N = 5;

L = 175;

omega = 0.015;

r = linspace(3, 15, 100);

xx = linspace(0, L, 100);

f = nan(length(xx));

for i = 1:length(xx)

    for j = i+1:length(xx)

        x = [xx(i);xx(j)];

        xn = [0; x; L];

        s1 = sum(cos(omega*xn*r),1);

        s2 = sum(sin(omega*xn*r),1);

        f(i,j) = max(s1.^2+s2.^2);

    end

end

mesh(f)

lofberg

Platinum Boarder

Posts: 2280

Last Edit: 2012/08/14 04:13 By lofberg.

The administrator has disabled public write access.

#6994

Re: A complicated convex problem, how to figure it out 9 Months, 1 Week ago	Karma: 0
Thank lofberg for your great help and valuable time. It seems there is no better way to figure out this problem.

xdkd1612

Fresh Boarder

Posts: 4

The administrator has disabled public write access.

#6996

Re: A complicated convex problem, how to figure it out 9 Months ago	Karma: 0
Use full post thanks

Thanksiok41

Fresh Boarder

Posts: 1

caregiver
senior care

The administrator has disabled public write access.

Page: 12

Kunena

General discussion

Help!!!

Moderators: jcg207