Questions Tagged With global-optimizationhttp://www.or-exchange.com/tags/global-optimization/?type=rssquestions tagged <span class="tag">global-optimization</span>enSun, 06 Nov 2016 02:40:27 -0500non-convex optimizationhttp://www.or-exchange.com/questions/14359/non-convex-optimization<p>Dear friends </p>
<p>I have a question about non convex models. I deal with a Mixed Integer Quadratic problem (non convex quadratic objective function with linear constraints- product of two continuous variables in the objective function makes it non convex). I want to know about the exact methods for solving this type of problems to obtain the global optimum<br>
</p>m_bkSun, 06 Nov 2016 02:40:27 -0500http://www.or-exchange.com/questions/14359/non-convex-optimizationglobal-optimizationFinding a feasible solution with negative objective function valuehttp://www.or-exchange.com/questions/11644/finding-a-feasible-solution-with-negative-objective-function-value<p>Consider the following convex continuous optimization problem:</p>
<p>min \(f(x)=\sqrt{(x'Qx)}-c'x\)
s.t. \(e'x \leq 1\)
\(x \geq 0,\)</p>
<p>where Q is positive definite, \(c\geq 0\) and \(e=(1,...,1)\).</p>
<p>I'm interested in any feasible point \(y\) satisfying \(f(y) < 0\). Assuming the \(f(z) < 0\) for the optimal solution \(z\). Is it true that there exists a vertex \(e_i\), such that \(f(e_i) < 0\)? For sure if this would not be true, there is a convex combination of the vertices with a negative objective function value, but how to find it?</p>LongWed, 11 Mar 2015 10:41:21 -0400http://www.or-exchange.com/questions/11644/finding-a-feasible-solution-with-negative-objective-function-valueglobal-optimizationconvex-optimizationDecide whether a convex, non-differentiable function attaints its minimum at zerohttp://www.or-exchange.com/questions/11116/decide-whether-a-convex-non-differentiable-function-attaints-its-minimum-at-zero<p>Hi, what would be the best way (theoretically and practically) to decide whether a convex but (only) in 0 non-differentiable function attains its global minimum in zero? A possibility would be to use a subgradient method still needing the subgradients. Is there a way to easily test, if 0 is the global minimizer? For example, is it to easy decide if there is a point where 0 is in its subdifferential or to decide if no descent direction in this point exists? Is it sufficient to evaluate for example all points (0+e_i) and (0-e_i) for all unit vectors e_i and show that the objective function value is non-negative?</p>LongTue, 20 Jan 2015 09:05:14 -0500http://www.or-exchange.com/questions/11116/decide-whether-a-convex-non-differentiable-function-attaints-its-minimum-at-zeroglobal-optimizationoptimizationnon-smoothconvexLinear and non-linear global optimalityhttp://www.or-exchange.com/questions/8349/linear-and-non-linear-global-optimality<ol>
<li>Solving a linear program always gives its global optimum.</li>
<li>
<p>Solving a non-linear program always gives its local optimum.</p>
</li>
<li>
<p>Benders decomposition applied to a linear program , gives global optimum</p>
</li>
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<p>Generalized benders decomposition (i.e. the subproblem is non-linear) gives local optimum.</p>
</li>
</ol>
<p>What are your views on the above observations? </p>spyimpTue, 23 Jul 2013 13:33:32 -0400http://www.or-exchange.com/questions/8349/linear-and-non-linear-global-optimalitybenders-decompositionglobal-optimizationbendersgeneralized[ANN] new global constrained optimization solver with discrete variableshttp://www.or-exchange.com/questions/4612/ann-new-global-constrained-optimization-solver-with-discrete-variables<p>hi all,
I've done support of discrete variables for <a href="http://openopt.org/interalg">interalg</a> - free solver with specifiable accuracy, you can take a look at an example <a href="http://trac.openopt.org/openopt/browser/PythonPackages/FuncDesigner/FuncDesigner/examples/exactGlobalMINLP.py">here</a>
It is written in Python + NumPy, and I hope its speed will be essentially increased when PyPy (Python with dynamic compilation) support for NumPy will be done (some parts of code are not vectorized and still use CPython cycles). </p>DmitreyMon, 16 Jan 2012 14:57:01 -0500http://www.or-exchange.com/questions/4612/ann-new-global-constrained-optimization-solver-with-discrete-variablesdiscrete-optimizationannouncementoptimization-softwareglobal-optimization