[SciPy-User] Problem using linprog

[Montgomery-Smith, Stephen]

Thank you.  That helps a little.  What is the definition of singular in
this context?

You definitely understood my problem.  The correct answer should have
been 0, as you correctly surmised.

I am trying to find a test to see if a union of half planes captures all
of Euclidean n-space.

On 11/26/18 5:40 PM, Chris F Waigl wrote:
> Hi Stephen,
> 
> The problem appears to be singular around the solution. A very quick
> exploration shows me that if you replace your upper bound b by a very
> small epsilon > 0, you get a stable result. 
> 
> For example: 
> b = np.zeros(8) + 0.001
> 
>  fun: -0.11764011575264395
>  message: 'Optimization terminated successfully.'
>  nit: 6
>  slack: array([0.        , 0.        , 0.40742577, 0.        , 0.40742577, 0.        , 0.        , 0.        , 0.88235988])
>  status: 0
>  success: True
>  x: array([0.        , 0.        , 0.        , 0.0834722 , 0.41811509, 0.11764012])
> 
> And for print(np.dot(A, result.x)) I get [ 0.001 0.001 -0.00307426 0.001
> -0.00307426 0.001 0.001 0.001 ]
> 
> In the objective function, y_2 = y_4 = -3.0742577 * epsilon, and the
> other 6 values also converge towards zero when epsilon -> 0 . 
> 
> If I read your problem correctly, your objective function is simply (-1)
> times x_5, the last element of x. The approach above would converge
> towards the trivial solution, x = 0, but your solution above minimizes
> f(x) by maximizing x_5 at 1. If we pick out an x_5, then the problem
> collapses to a new problems to find [x_0 ... x_4] so that A[:, 0:7] *
> [x_0 ... x_4]' < b, where b is (-1) * the last column of your A. But the
> objective function is now indeterminate, so there is nothing to optimize.  
> 
> HTH,
> 
> Chris
> 
> On Mon, Nov 26, 2018 at 11:43 AM Montgomery-Smith, Stephen
> <stephen at missouri.edu <mailto:stephen at missouri.edu>> wrote:
> 
>     I am trying to solve a linear programming problem.  The constraint is of
>     the form A.x <= 0.  But linprog gives an answer that doesn't satisfy the
>     constraint.
> 
>     The attached program gives A.x as
> 
>     [-2.32109228  2.32017594  4.71436317  3.6433767  -4.26629574  2.32384597
>      -1.96166184 -4.96206197]
> 
>     which definitely doesn't satisfy the constraint.  Is this a bug, or some
>     subtle floating point error?
> 
>     Program follows (also as attachment):
> 
>     from scipy.optimize import linprog
>     import numpy as np
> 
>     A = [[0.5919650431077654, -0.5271408402306996, 0.6096719792636803,
>     1.2379670854947114, 0.2656040423387233, -0.972363043155988],
>     [-0.5914974900295467, -0.5266568950860249, 0.6105433925177587,
>     1.258297461476007, -0.285688537323182, 0.9726089241528251],
>     [-0.593015674004932, 0.5280764198909397, 0.6078385518701857,
>     -1.1964319796886902, -0.2223431679788034, -0.9740888117098865],
>     [0.5935986604093653, 0.5285277328950352, 0.6068764832493029,
>     -1.1752312553140132, 0.19916734259906424, 0.976063912714949],
>     [0.593015674004932, -0.5280764198909397, -0.6078385518701857,
>     -1.1964319796886902, -0.2223431679788034, -0.9740888117098865],
>     [-0.5935986604093653, -0.5285277328950352, -0.6068764832493029,
>     -1.1752312553140132, 0.19916734259906424, 0.976063912714949],
>     [-0.5919650431077654, 0.5271408402306996, -0.6096719792636803,
>     1.2379670854947114, 0.2656040423387233, -0.972363043155988],
>     [0.5914974900295467, 0.5266568950860249, -0.6105433925177587,
>     1.258297461476007, -0.285688537323182, 0.9726089241528251]]
>     e = [0, 0, 0, 0, 0, -1]
>     bounds = [(None, None), (None, None), (None, None), (None, None), (None,
>     None), (0, 1)]
>     b = [0]*len(A)
>     result = linprog(e, A_ub = A, b_ub = b, bounds = bounds)
>     print np.matmul(A, result.x)
> 
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> 
> 
> -- 
> Chris Waigl . chris.waigl at gmail.com <mailto:chris.waigl at gmail.com> .
> chris at lascribe.net <mailto:chris at lascribe.net>
> http://eggcorns.lascribe.net . http://chryss.eu
> 
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