Timeline for Obtaining a feasible solution for underdetermined system of linear equations satisfying inequality constraints
Current License: CC BY-SA 3.0
19 events
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| Mar 1, 2018 at 19:28 | history | tweeted | twitter.com/StackSciComp/status/969293386007097344 | ||
| Feb 27, 2018 at 22:30 | vote | accept | Dr Krishnakumar Gopalakrishnan | ||
| Feb 27, 2018 at 22:30 | answer | added | Beni Bogosel | timeline score: 2 | |
| Feb 27, 2018 at 21:38 | comment | added | Mark L. Stone | You can save yourself the "pain" and error propensity of figuring out how to use quadprog by using CVX. cvx_begin;variable x(9);minimize(norm(x));A*x == b;abs(sum(x(1:3) - k) <= c1;abs(sum(x(7:9) - k) <= c2;cvx_end At the conclusion of which x will contain its optimal value and be available in MATLAB. | |
| Feb 27, 2018 at 18:57 | history | edited | Dr Krishnakumar Gopalakrishnan | CC BY-SA 3.0 |
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| Feb 27, 2018 at 18:23 | history | edited | Dr Krishnakumar Gopalakrishnan | CC BY-SA 3.0 |
deleted 4 characters in body
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| Feb 27, 2018 at 18:17 | history | edited | Dr Krishnakumar Gopalakrishnan | CC BY-SA 3.0 |
added 26 characters in body
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| Feb 27, 2018 at 18:06 | comment | added | Dr Krishnakumar Gopalakrishnan | Let us continue this discussion in chat. | |
| Feb 27, 2018 at 18:05 | history | edited | Dr Krishnakumar Gopalakrishnan | CC BY-SA 3.0 |
Changed the question so as to truly reflect the detail that we are possibly working with a linear programming problem here
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| Feb 27, 2018 at 17:57 | comment | added | Dr Krishnakumar Gopalakrishnan |
@RodrigodeAzevedo Thank you. That does indeed work! Just tried it. The solution is unique because it is a linear programming problem. If you write your final comments as an answer, I can accept it for the benefit of whoever lands here in the future through a google search. Yes, 0 $\in \mathbb{R}^{9\times1}$ here
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| Feb 27, 2018 at 17:30 | comment | added | Rodrigo de Azevedo |
Correct if 0 denotes a zero vector.
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| Feb 27, 2018 at 17:26 | comment | added | Dr Krishnakumar Gopalakrishnan |
@RodrigodeAzevedo thank you. That indeed makes sense. So first I convert the inequalities to be $\le$ and then apply linprog uk.mathworks.com/help/optim/ug/linprog.html from the optimization toolbox? x = linprog(f,A,b,Aeq,beq) wherein f = 0 ,right?
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| Feb 27, 2018 at 16:14 | comment | added | Rodrigo de Azevedo | Why not write $-c_1 \leq x_1 + x_2 + x_3 - k \leq c_1$? It is the conjunction of two linear inequalities. Also, you don't have an objective function. There is nothing to minimize. You have linear equality and inequality constraints. Deciding whether there exists a feasible solution can be done via linear programming. | |
| Feb 27, 2018 at 16:06 | comment | added | Dr Krishnakumar Gopalakrishnan |
@RodrigodeAzevedo yes. My inequality constraints are mostly linear, i.e. they are of the form $|x_1 + x_2 + x_3 - k| \le c_1$, where $k$ and $c_1$ are just scalar numerical values. The non-linearity comes solely due to absolute value function. Is there a way of converting this to a 'quadratic' or other well-posed linear problem? I too feel that using a general NLP solver like fmincon is like using a sledgehammer rather than a scalpel.
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| Feb 27, 2018 at 6:47 | comment | added | Rodrigo de Azevedo | "Nonlinear" is too broad. Quadratic? Polynomial? And if the system is underdetermined, why use least-squares? Why not least-norm? | |
| Feb 26, 2018 at 17:49 | comment | added | Tyler Olsen |
Well, I think you have answered your own question. $g(x) = \|Ax-b\|_2$ is a scalar function, and fmincon can certainly handle problems of the form $\min_x g(x) \;\; s.t \;\; f_1(x)\le c_1, \;\; f_2(x) \le c_2$.
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| Feb 26, 2018 at 16:56 | comment | added | Dr Krishnakumar Gopalakrishnan | @Rahul, I doubt that is even possible. fmincon minimizes only a scalar function, see here uk.mathworks.com/help/optim/ug/fmincon.html . | |
| Feb 26, 2018 at 16:00 | comment | added | user3883 |
Apply fmincon to the normal equations?
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| Feb 26, 2018 at 14:35 | history | asked | Dr Krishnakumar Gopalakrishnan | CC BY-SA 3.0 |