Questions Tagged With discrete-optimizationhttp://www.or-exchange.com/tags/discrete-optimization/?type=rssquestions tagged <span class="tag">discrete-optimization</span>enSat, 07 Nov 2015 06:25:47 -0500Lagrangian Relaxation Fisherhttp://www.or-exchange.com/questions/12991/lagrangian-relaxation-fisher<p>This is one of the most well-known papers on Lagrangian relaxation , produced by Fisher:<br>
<a href="http://yalma.fime.uanl.mx/~roger/work/teaching/mecbs5100/papers/lagrangean%20relaxation/int-1985-Fisher.pdf">http://yalma.fime.uanl.mx/~roger/work/teaching/mecbs5100/papers/lagrangean%20relaxation/int-1985-Fisher.pdf</a></p>
<p>If you see, on page 13 (the number of the page as it is written on the document), it says that the derivative of the Lagrangian Problem function is : 8x1 + 2x2 + x3+ 4x4 - 10. But if you calculate it , you find : -8x1 - 2x2 - x3- 4x4 + 10.
Did he do such a basic mistake, or am I so wrong here ?</p>spyimpSat, 07 Nov 2015 06:25:47 -0500http://www.or-exchange.com/questions/12991/lagrangian-relaxation-fisherdiscrete-optimizationstochastic-optimizationlagrangian-relaxationAn approach for the optimization problem with polynomial constraints?http://www.or-exchange.com/questions/12724/an-approach-for-the-optimization-problem-with-polynomial-constraints<p>I have a problem where the objective function is linear and the constraints have polynomials. So, my question is what are the main approaches to this issue? I can construct a small example, just to illustrate it.</p>
<p>$$ \max \sum_{i} a_i x_i - \sum_{j} b_j y_j $$</p>
<p>$$\qquad c_1 x_i + c_2 x_i^2 + c_3 x_i^3 +\ldots + c_k x_i^k = \sum_{j} d_j y_j, \quad \forall i\in N $$</p>
<p>$$\qquad x_i \geq 0, \quad i\in N $$</p>
<p>$$\qquad y_j \in \{0,1\}, \quad\forall j\in M $$</p>RDjMMon, 24 Aug 2015 19:09:25 -0400http://www.or-exchange.com/questions/12724/an-approach-for-the-optimization-problem-with-polynomial-constraintsdiscrete-optimizationnonlinear-optimizationpolynomials[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