Hi,
I have a quadratic optimization problem with only bound constraint (i.e. lb
Dear Mohanad,
I suggest you a links and attached files in topics.
-Constrained quadratic programming with box/linear constraints - ALGLIB
www.alglib.net/optimization/quadraticprogramming.php
-SOLVING GENERAL CONVEX QP PROBLEMS VIA AN EXACT ...
www.mathematik.tu-darmstadt.de/fbereiche/numerik/staff/spellucci/papers/qp.ps
-NLopt Introduction - AbInitio
ab-initio.mit.edu/wiki/index.php/NLopt_Introduction
Best regards
Linear constraints are more complex than box constraints (which are very simple forms of linear constraints), so I do not see why you would want that conversion. Box constraints are also very easy to handle: if you have a favourite search direction you can use a line search methodology based on that and use the very simple Euclidean projections to produce a very fast (per iteration) methodology. As an example (although it may be slow), simply use the steepest descent direction, and use the Armijo step length rule based on the starting point and the result you get by taking a step along the negative gradient, followed be the very simple Euclidian projection onto the feasible set. (The last operation is very fast, since all you need to do is to compare each coordinate's value and if one value is too small or too large you simply bring it back to being feasible.)
In addition to the answers above, I find the formulation tips and tricks in the following quite useful:
(see Ch 6)
AIMMS Modeling Guide - Linear Programming Tricks
For a free down load of the complete book in pdf format, see www.aimms.com
You may read my article in Researchgate
Constrained LQR Design Using Interior-Point Arc-Search Method for Convex Quadratic Programming with Box Constraints
Best,
Yaguang Yang
You are facing a simple Non lineal Programming task. For it solution you can use any of the numeric Non linear Programming methods, by example, the Localization of the extreme of the function of one variable, if it is a single independent variable problem or the Exploration if it is a problem of more than an independent variable. These methods you can find in any book devoted to the numeric optimization methods..
Best wishes, Jose Arzola
Completing the previous answer: I have told about the Exploration in a Net of Variables method, that requires the inferior and superior bounds determination to each variable. The objective function could have any form, including quadratic functions as a particular case.
@Mohanad
I guess (I can be wrong too) that you want use the slack variable as uncertainty parameter.
Whatever you want do, you have to write two linear contraints. i.e.
lb >> with slack variable: sv1 * x >>> with slack variable: sv2 * x
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