# [SciPy-User] Problem using linprog

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## [SciPy-User] Problem using linprog

 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) _______________________________________________ SciPy-User mailing list [hidden email] https://mail.python.org/mailman/listinfo/scipy-user test.py (1K) Download Attachment
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## Re: Problem using linprog

 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,ChrisOn Mon, Nov 26, 2018 at 11:43 AM Montgomery-Smith, Stephen <[hidden email]> 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) _______________________________________________ SciPy-User mailing list [hidden email] https://mail.python.org/mailman/listinfo/scipy-user -- Chris Waigl . [hidden email] . [hidden email]http://eggcorns.lascribe.net . http://chryss.eu _______________________________________________ SciPy-User mailing list [hidden email] https://mail.python.org/mailman/listinfo/scipy-user