MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi

### Discover what MATLAB® can do for your career.

 Subject: how to solve quadratic minimization problem with quadratic equality constraints? Date: 11 Jul, 2012 02:16:54 Message: 1 of 10 Hello everyone, Nowadays, I have faced a quadratic minimization problem with quadratic equality constraints. Is it a non-concave constrained optimization problem which CPLEX cannot handle? If so, how to solve? Is there any solver or software available? Could you suggest something? Many thanks.
 Subject: how to solve quadratic minimization problem with quadratic Date: 11 Jul, 2012 05:32:35 Message: 2 of 10 On Tuesday, July 10, 2012 9:16:54 PM UTC-5, Hycere Hung wrote: > Hello everyone, > Nowadays, I have faced a quadratic minimization problem with quadratic equality constraints. Is it a non-concave constrained optimization problem which CPLEX cannot handle? If so, how to solve? Is there any solver or software available? > Could you suggest something? > Many thanks. help the fmincon function
 Subject: how to solve quadratic minimization problem with quadratic From: Hycere Hung Date: 11 Jul, 2012 07:02:30 Message: 3 of 10 在 2012年7月11日星期三UTC+8下午1时32分35秒，（未知）写道： > On Tuesday, July 10, 2012 9:16:54 PM UTC-5, Hycere Hung wrote: > > Hello everyone, > > Nowadays, I have faced a quadratic minimization problem with quadratic equality constraints. Is it a non-concave constrained optimization problem which CPLEX cannot handle? If so, how to solve? Is there any solver or software available? > > Could you suggest something? > > Many thanks. > > > help the fmincon function Okay, millions of thx.
 Subject: how to solve quadratic minimization problem with quadratic equality From: Marcelo Marazzi Date: 11 Jul, 2012 14:26:07 Message: 4 of 10 Hi: For your type of problem, both first and second derivatives are readily available. So, ideally, you can calculate those and pass them to the solver. Below is a pointer to an example in the documentation on how to do this. -Marcelo --- Example: Constrained Minimization Using fmincon's Interior-Point Algorithm with Analytic Hessian http://www.mathworks.com/help/toolbox/optim/ug/brn4nh7.html#bri8026 On 7/10/2012 10:16 PM, honeyhycere@gmail.com wrote: > Hello everyone, > Nowadays, I have faced a quadratic minimization problem with quadratic equality constraints. Is it a non-concave constrained optimization problem which CPLEX cannot handle? If so, how to solve? Is there any solver or software available? > Could you suggest something? > Many thanks. >
 Subject: how to solve quadratic minimization problem with quadratic equality constraints? From: Matt J Date: 11 Jul, 2012 15:20:11 Message: 5 of 10 honeyhycere@gmail.com wrote in message <8857c2c6-a43c-4c0f-8342-8b2e8e415215@googlegroups.com>... > Hello everyone, > Nowadays, I have faced a quadratic minimization problem with quadratic equality constraints. Is it a non-concave constrained optimization problem which CPLEX cannot handle? If so, how to solve? Is there any solver or software available? =========== This problem has an analytically known solution, which you could use if your problem isn't too large: http://www.mathworks.com/matlabcentral/fileexchange/27596-least-square-with-2-norm-constraint
 Subject: how to solve quadratic minimization problem with quadratic From: Hycere Hung Date: 12 Jul, 2012 00:56:16 Message: 6 of 10 在 2012年7月11日星期三UTC+8下午10时26分07秒，Marcelo Marazzi写道： > Hi: > > For your type of problem, both first and second derivatives are readily > available. So, ideally, you can calculate those and pass them to the > solver. Below is a pointer to an example in the documentation on how to > do this. > > -Marcelo > > --- > Example: Constrained Minimization Using fmincon's Interior-Point > Algorithm with Analytic Hessian > http://www.mathworks.com/help/toolbox/optim/ug/brn4nh7.html#bri8026 > > On 7/10/2012 10:16 PM, honeyhycere@gmail.com wrote: > > Hello everyone, > > Nowadays, I have faced a quadratic minimization problem with quadratic equality constraints. Is it a non-concave constrained optimization problem which CPLEX cannot handle? If so, how to solve? Is there any solver or software available? > > Could you suggest something? > > Many thanks. > > Thank you, Marcelo. I will give it a try.
 Subject: how to solve quadratic minimization problem with quadratic From: Hycere Hung Date: 12 Jul, 2012 01:02:21 Message: 7 of 10 在 2012年7月11日星期三UTC+8下午11时20分11秒，Matt J 写道： > honeyhycere@gmail.com wrote in message <8857c2c6-a43c-4c0f-8342-8b2e8e415215@googlegroups.com>... > > Hello everyone, > > Nowadays, I have faced a quadratic minimization problem with quadratic equality constraints. Is it a non-concave constrained optimization problem which CPLEX cannot handle? If so, how to solve? Is there any solver or software available? > =========== > > This problem has an analytically known solution, which you could use if your problem isn't too large: > > http://www.mathworks.com/matlabcentral/fileexchange/27596-least-square-with-2-norm-constraint Hi, Matt, In my problem, the H is semi-definite, and the quadratic equality constraint has the form of l*x + x'*Q*x = r. In this case, i don't think spherelsq can handle this.
 Subject: how to solve quadratic minimization problem with quadratic From: Bruno Luong Date: 12 Jul, 2012 01:52:36 Message: 8 of 10 Hycere Hung wrote in message <0ab635fa-2671-4b69-8d14-0f9135f164df@googlegroups.com>... > > Hi, Matt, > In my problem, the H is semi-definite, and the quadratic equality constraint has the form of l*x + x'*Q*x = r. In this case, i don't think spherelsq can handle this. Assuming Q is symmetric definite positive , the constraint l*x + x'*Q*x = r, (2) can be rewritten to | C*x + d |^2 = p^2, where   C = sqrtm(Q) d = 1/2 * (C\l') p^2 - |d|^2 = r. (note: should double check my formula for error) So after changing the variable y := C*x + d, the problem becomes minimizing quadratic with 2-norm constraint |y| = p. Rather than changing variable, you could directly derive the QEP equation by Euler-Lagrage on (2) using the same technique as in the paper I cited. Bruno (author of the FEX in question)
 Subject: how to solve quadratic minimization problem with quadratic From: Hycere Hung Date: 12 Jul, 2012 06:03:26 Message: 9 of 10 在 2012年7月12日星期四UTC+8上午9时52分36秒，Bruno Luong写道： > Hycere Hung wrote in message <0ab635fa-2671-4b69-8d14-0f9135f164df@googlegroups.com>... > > > > > Hi, Matt, > > In my problem, the H is semi-definite, and the quadratic equality constraint has the form of l*x + x'*Q*x = r. In this case, i don't think spherelsq can handle this. > > Assuming Q is symmetric definite positive , the constraint > > l*x + x'*Q*x = r, (2) > > can be rewritten to > > | C*x + d |^2 = p^2, where > > C = sqrtm(Q) > d = 1/2 * (C\l') > p^2 - |d|^2 = r. (note: should double check my formula for error) > > So after changing the variable y := C*x + d, the problem becomes minimizing quadratic with 2-norm constraint |y| = p. > > Rather than changing variable, you could directly derive the QEP equation by Euler-Lagrage on (2) using the same technique as in the paper I cited. > > Bruno (author of the FEX in question) Many thanks for your kindly help, Bruno I will try it these days
 Subject: how to solve quadratic minimization problem with quadratic From: Hycere Hung Date: 12 Jul, 2012 05:59:21 Message: 10 of 10 在 2012年7月12日星期四UTC+8上午9时52分36秒，Bruno Luong写道： > Hycere Hung wrote in message <0ab635fa-2671-4b69-8d14-0f9135f164df@googlegroups.com>... > > > > > Hi, Matt, > > In my problem, the H is semi-definite, and the quadratic equality constraint has the form of l*x + x'*Q*x = r. In this case, i don't think spherelsq can handle this. > > Assuming Q is symmetric definite positive , the constraint > > l*x + x'*Q*x = r, (2) > > can be rewritten to > > | C*x + d |^2 = p^2, where > > C = sqrtm(Q) > d = 1/2 * (C\l') > p^2 - |d|^2 = r. (note: should double check my formula for error) > > So after changing the variable y := C*x + d, the problem becomes minimizing quadratic with 2-norm constraint |y| = p. > > Rather than changing variable, you could directly derive the QEP equation by Euler-Lagrage on (2) using the same technique as in the paper I cited. > > Bruno (author of the FEX in question) Many thanks for your kindly help, Bruno I will try it these days