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copied!<p>Based on the comment from Robert Kern, I have removed my previous answer. Here are the constraints as continuous functions:</p> <pre><code>b1 = lambda x: x[4]-x[0] if x[4]<1.2*x[0] else 1.4*x[0]-x[4] b2 = lambda x: x[5]-x[1] if x[5]<1.2*x[1] else 1.4*x[1]-x[5] b3 = lambda x: x[2]-x[3] </code></pre> <p>Note: Python 2.5 or greater is required for this syntax.<sup>1</sup></p> <p>To get the constraint <code>a<=e<=1.4*a</code>, note that <code>1.2*a</code> is the halfway point between <code>a</code> and <code>1.4*a</code>.</p> <p>Below this point, that is, all <code>e<1.2*a</code>, we use the continuous function <code>e-a</code>. Thus the overall constraint function is negative when <code>e<a</code>, handling the lower out-of-bounds condition, zero on the lower boundary <code>e==a</code>, and then positive for <code>e>a</code> up to the halfway point.</p> <p>Above the halfway point, that is, all <code>e>1.2*a</code>, we use instead the continuous function <code>1.4*a-e</code>. This means the overall constraint function is is negative when <code>e>1.4*a</code>, handling the upper out-of-bounds condition, zero on the upper boundary <code>e==1.4*a</code>, and then positive when <code>e<1.4*a</code>, down to the halfway point.</p> <p>At the halfway point, where <code>e==1.2*a</code>, both functions have the same value. This means that the overall function is continuous.</p> <p>Reference: <a href="http://projects.scipy.org/scipy/attachment/ticket/565/slsqp.py" rel="nofollow noreferrer">documentation for <code>ieqcons</code></a>.</p> <p><sup><strong>1</strong> - Here is pre-Python 2.5 syntax: <code>b1 = lambda x: (1.4*x[0]-x[4], x[4]-x[0])[x[4]<1.2*x[0]]</code></sup></p>

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