Solve contrained nonlinear optimization problem by MATLAB [closed]

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I know in MATLAB there is a fmincon to solve this kind of problem. But I really don't know how to use it for my problem.

Question 1: Find optimal $u$ to

$u^TDx-fracmu2 |u|^2 rightarrow max$

$|u_i| le 1$

where $x$ - given 1D column vector, $mu$ - const, |.| - $L_2$ norm, $D$ - gradient operator, $u$ - 1D column vector.

Question 2: Do above problem and below problem have same optimum?

$-(u^TDx-fracmu2 |u|^2) rightarrow min$

$|u_i| le 1$

If without constraint, this is right. However, there is constraint, do they have same optimum? I don't want to formulate the dual problem.

optimization matlab nonlinear-optimization numerical-optimization

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edited Aug 6 at 15:38

asked Aug 6 at 4:04

HTCom

1013

closed as off-topic by Theoretical Economist, Taroccoesbrocco, Shailesh, José Carlos Santos, Key Flex Aug 6 at 16:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Theoretical Economist, Taroccoesbrocco, Shailesh, José Carlos Santos, Key Flex

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Have you read the documentation on fmincon? It should tell you everything you need to know.
  – Theoretical Economist
  Aug 6 at 5:10
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  This is a convex quadratic optimization problem for which the optimization toolbox (as well as similar toolboxes from external vendors) will be much more suitable in terms of performance and accuracy than fmincon. Search under quadprog.
  – Michal Adamaszek
  Aug 6 at 5:28
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Can I transfer this problem to min by add minus before functional and unchange the condition? I don't want to formulate the dual problem. If without contraint, $frightarrow max$ and $-frightarrow min$ have same optimum, but there is a constraint.
  – HTCom
  Aug 6 at 5:34
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  For Q2, the answer is yes. You can multiply your objective function by $-1$ and minimise it subject to the same constraints. I agree with Michael's comment that you're better off using quadprog instead of fmincon.
  – Theoretical Economist
  Aug 6 at 13:14
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

I know in MATLAB there is a fmincon to solve this kind of problem. But I really don't know how to use it for my problem.

Question 1: Find optimal $u$ to

$u^TDx-fracmu2 |u|^2 rightarrow max$

$|u_i| le 1$

where $x$ - given 1D column vector, $mu$ - const, |.| - $L_2$ norm, $D$ - gradient operator, $u$ - 1D column vector.

Question 2: Do above problem and below problem have same optimum?

$-(u^TDx-fracmu2 |u|^2) rightarrow min$

$|u_i| le 1$

If without constraint, this is right. However, there is constraint, do they have same optimum? I don't want to formulate the dual problem.

optimization matlab nonlinear-optimization numerical-optimization

share|cite|improve this question

edited Aug 6 at 15:38

asked Aug 6 at 4:04

HTCom

1013

closed as off-topic by Theoretical Economist, Taroccoesbrocco, Shailesh, José Carlos Santos, Key Flex Aug 6 at 16:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Theoretical Economist, Taroccoesbrocco, Shailesh, José Carlos Santos, Key Flex

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Have you read the documentation on fmincon? It should tell you everything you need to know.
  – Theoretical Economist
  Aug 6 at 5:10
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  This is a convex quadratic optimization problem for which the optimization toolbox (as well as similar toolboxes from external vendors) will be much more suitable in terms of performance and accuracy than fmincon. Search under quadprog.
  – Michal Adamaszek
  Aug 6 at 5:28
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Can I transfer this problem to min by add minus before functional and unchange the condition? I don't want to formulate the dual problem. If without contraint, $frightarrow max$ and $-frightarrow min$ have same optimum, but there is a constraint.
  – HTCom
  Aug 6 at 5:34
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  For Q2, the answer is yes. You can multiply your objective function by $-1$ and minimise it subject to the same constraints. I agree with Michael's comment that you're better off using quadprog instead of fmincon.
  – Theoretical Economist
  Aug 6 at 13:14
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I know in MATLAB there is a fmincon to solve this kind of problem. But I really don't know how to use it for my problem.

Question 1: Find optimal $u$ to

$u^TDx-fracmu2 |u|^2 rightarrow max$

$|u_i| le 1$

where $x$ - given 1D column vector, $mu$ - const, |.| - $L_2$ norm, $D$ - gradient operator, $u$ - 1D column vector.

Question 2: Do above problem and below problem have same optimum?

$-(u^TDx-fracmu2 |u|^2) rightarrow min$

$|u_i| le 1$

If without constraint, this is right. However, there is constraint, do they have same optimum? I don't want to formulate the dual problem.

optimization matlab nonlinear-optimization numerical-optimization

share|cite|improve this question

edited Aug 6 at 15:38

asked Aug 6 at 4:04

HTCom

1013

I know in MATLAB there is a fmincon to solve this kind of problem. But I really don't know how to use it for my problem.

Question 1: Find optimal $u$ to

$u^TDx-fracmu2 |u|^2 rightarrow max$

$|u_i| le 1$

where $x$ - given 1D column vector, $mu$ - const, |.| - $L_2$ norm, $D$ - gradient operator, $u$ - 1D column vector.

Question 2: Do above problem and below problem have same optimum?

$-(u^TDx-fracmu2 |u|^2) rightarrow min$

$|u_i| le 1$

If without constraint, this is right. However, there is constraint, do they have same optimum? I don't want to formulate the dual problem.

optimization matlab nonlinear-optimization numerical-optimization

share|cite|improve this question

edited Aug 6 at 15:38

asked Aug 6 at 4:04

HTCom

1013

share|cite|improve this question

share|cite|improve this question

edited Aug 6 at 15:38

edited Aug 6 at 15:38

edited Aug 6 at 15:38

asked Aug 6 at 4:04

HTCom

1013

asked Aug 6 at 4:04

HTCom

1013

asked Aug 6 at 4:04

HTCom

1013

1013

closed as off-topic by Theoretical Economist, Taroccoesbrocco, Shailesh, José Carlos Santos, Key Flex Aug 6 at 16:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Theoretical Economist, Taroccoesbrocco, Shailesh, José Carlos Santos, Key Flex

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Theoretical Economist, Taroccoesbrocco, Shailesh, José Carlos Santos, Key Flex Aug 6 at 16:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Theoretical Economist, Taroccoesbrocco, Shailesh, José Carlos Santos, Key Flex

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Have you read the documentation on fmincon? It should tell you everything you need to know.
  – Theoretical Economist
  Aug 6 at 5:10
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  This is a convex quadratic optimization problem for which the optimization toolbox (as well as similar toolboxes from external vendors) will be much more suitable in terms of performance and accuracy than fmincon. Search under quadprog.
  – Michal Adamaszek
  Aug 6 at 5:28
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Can I transfer this problem to min by add minus before functional and unchange the condition? I don't want to formulate the dual problem. If without contraint, $frightarrow max$ and $-frightarrow min$ have same optimum, but there is a constraint.
  – HTCom
  Aug 6 at 5:34
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  For Q2, the answer is yes. You can multiply your objective function by $-1$ and minimise it subject to the same constraints. I agree with Michael's comment that you're better off using quadprog instead of fmincon.
  – Theoretical Economist
  Aug 6 at 13:14
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Have you read the documentation on fmincon? It should tell you everything you need to know.
  – Theoretical Economist
  Aug 6 at 5:10
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  This is a convex quadratic optimization problem for which the optimization toolbox (as well as similar toolboxes from external vendors) will be much more suitable in terms of performance and accuracy than fmincon. Search under quadprog.
  – Michal Adamaszek
  Aug 6 at 5:28
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Can I transfer this problem to min by add minus before functional and unchange the condition? I don't want to formulate the dual problem. If without contraint, $frightarrow max$ and $-frightarrow min$ have same optimum, but there is a constraint.
  – HTCom
  Aug 6 at 5:34
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  For Q2, the answer is yes. You can multiply your objective function by $-1$ and minimise it subject to the same constraints. I agree with Michael's comment that you're better off using quadprog instead of fmincon.
  – Theoretical Economist
  Aug 6 at 13:14
  

  
  
  
  

1

1

Have you read the documentation on fmincon? It should tell you everything you need to know.
– Theoretical Economist
Aug 6 at 5:10

Have you read the documentation on fmincon? It should tell you everything you need to know.
– Theoretical Economist
Aug 6 at 5:10

1

1

This is a convex quadratic optimization problem for which the optimization toolbox (as well as similar toolboxes from external vendors) will be much more suitable in terms of performance and accuracy than fmincon. Search under quadprog.
– Michal Adamaszek
Aug 6 at 5:28

This is a convex quadratic optimization problem for which the optimization toolbox (as well as similar toolboxes from external vendors) will be much more suitable in terms of performance and accuracy than fmincon. Search under quadprog.
– Michal Adamaszek
Aug 6 at 5:28

1

1

Can I transfer this problem to min by add minus before functional and unchange the condition? I don't want to formulate the dual problem. If without contraint, $frightarrow max$ and $-frightarrow min$ have same optimum, but there is a constraint.
– HTCom
Aug 6 at 5:34

Can I transfer this problem to min by add minus before functional and unchange the condition? I don't want to formulate the dual problem. If without contraint, $frightarrow max$ and $-frightarrow min$ have same optimum, but there is a constraint.
– HTCom
Aug 6 at 5:34

1

1

For Q2, the answer is yes. You can multiply your objective function by $-1$ and minimise it subject to the same constraints. I agree with Michael's comment that you're better off using quadprog instead of fmincon.
– Theoretical Economist
Aug 6 at 13:14

For Q2, the answer is yes. You can multiply your objective function by $-1$ and minimise it subject to the same constraints. I agree with Michael's comment that you're better off using quadprog instead of fmincon.
– Theoretical Economist
Aug 6 at 13:14

add a comment | 

1 Answer
1

active

oldest

votes

up vote
2
down vote

Most optimization solvers require an objective function (by default) in minimization form. Multiplying a maximization by negative one is one way to reliably transform the objective to a minimization statement, even with constraints. I created an fmincon tutorial with source code (see method #2) for a problem with an objective function, equality constraint, and an inequality constraint or you can use MathWorks' fmincon or quadprog documentation.

If you do solve this problem numerically, you should avoid the use of an absolute value operator $left | u_i right |<1$ as an inequality constraint but instead use an upper and lower bound on the variable ($u_ilt 1$ and $u_igt -1$). Using an absolute value operator may cause problems for gradient based solvers that require continuous first and second derivatives.

share|cite|improve this answer

answered Aug 6 at 12:52

John Hedengren

413

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How can I formulate objective function in Matlab with undefined number of argument? $u=(u_1, u_2, ..., u_n)$ Just like this objective = @(u) u(1)+u(2)+.......+u(n)+u(1)*u(1)+u(2)*u(2)+....+u(n)*u(n);
  – HTCom
  Aug 6 at 15:32
  
  

  
  
  
  

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
2
down vote

Most optimization solvers require an objective function (by default) in minimization form. Multiplying a maximization by negative one is one way to reliably transform the objective to a minimization statement, even with constraints. I created an fmincon tutorial with source code (see method #2) for a problem with an objective function, equality constraint, and an inequality constraint or you can use MathWorks' fmincon or quadprog documentation.

If you do solve this problem numerically, you should avoid the use of an absolute value operator $left | u_i right |<1$ as an inequality constraint but instead use an upper and lower bound on the variable ($u_ilt 1$ and $u_igt -1$). Using an absolute value operator may cause problems for gradient based solvers that require continuous first and second derivatives.

share|cite|improve this answer

answered Aug 6 at 12:52

John Hedengren

413

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How can I formulate objective function in Matlab with undefined number of argument? $u=(u_1, u_2, ..., u_n)$ Just like this objective = @(u) u(1)+u(2)+.......+u(n)+u(1)*u(1)+u(2)*u(2)+....+u(n)*u(n);
  – HTCom
  Aug 6 at 15:32
  
  

  
  
  
  

add a comment | 

up vote
2
down vote

Most optimization solvers require an objective function (by default) in minimization form. Multiplying a maximization by negative one is one way to reliably transform the objective to a minimization statement, even with constraints. I created an fmincon tutorial with source code (see method #2) for a problem with an objective function, equality constraint, and an inequality constraint or you can use MathWorks' fmincon or quadprog documentation.

If you do solve this problem numerically, you should avoid the use of an absolute value operator $left | u_i right |<1$ as an inequality constraint but instead use an upper and lower bound on the variable ($u_ilt 1$ and $u_igt -1$). Using an absolute value operator may cause problems for gradient based solvers that require continuous first and second derivatives.

share|cite|improve this answer

answered Aug 6 at 12:52

John Hedengren

413

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How can I formulate objective function in Matlab with undefined number of argument? $u=(u_1, u_2, ..., u_n)$ Just like this objective = @(u) u(1)+u(2)+.......+u(n)+u(1)*u(1)+u(2)*u(2)+....+u(n)*u(n);
  – HTCom
  Aug 6 at 15:32
  
  

  
  
  
  

add a comment | 

up vote
2
down vote

up vote
2
down vote

Most optimization solvers require an objective function (by default) in minimization form. Multiplying a maximization by negative one is one way to reliably transform the objective to a minimization statement, even with constraints. I created an fmincon tutorial with source code (see method #2) for a problem with an objective function, equality constraint, and an inequality constraint or you can use MathWorks' fmincon or quadprog documentation.

If you do solve this problem numerically, you should avoid the use of an absolute value operator $left | u_i right |<1$ as an inequality constraint but instead use an upper and lower bound on the variable ($u_ilt 1$ and $u_igt -1$). Using an absolute value operator may cause problems for gradient based solvers that require continuous first and second derivatives.

share|cite|improve this answer

answered Aug 6 at 12:52

John Hedengren

413

Most optimization solvers require an objective function (by default) in minimization form. Multiplying a maximization by negative one is one way to reliably transform the objective to a minimization statement, even with constraints. I created an fmincon tutorial with source code (see method #2) for a problem with an objective function, equality constraint, and an inequality constraint or you can use MathWorks' fmincon or quadprog documentation.

If you do solve this problem numerically, you should avoid the use of an absolute value operator $left | u_i right |<1$ as an inequality constraint but instead use an upper and lower bound on the variable ($u_ilt 1$ and $u_igt -1$). Using an absolute value operator may cause problems for gradient based solvers that require continuous first and second derivatives.

share|cite|improve this answer

answered Aug 6 at 12:52

John Hedengren

413

share|cite|improve this answer

share|cite|improve this answer

answered Aug 6 at 12:52

John Hedengren

413

answered Aug 6 at 12:52

John Hedengren

413

answered Aug 6 at 12:52

John Hedengren

413

413

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How can I formulate objective function in Matlab with undefined number of argument? $u=(u_1, u_2, ..., u_n)$ Just like this objective = @(u) u(1)+u(2)+.......+u(n)+u(1)*u(1)+u(2)*u(2)+....+u(n)*u(n);
  – HTCom
  Aug 6 at 15:32
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  How can I formulate objective function in Matlab with undefined number of argument? $u=(u_1, u_2, ..., u_n)$ Just like this objective = @(u) u(1)+u(2)+.......+u(n)+u(1)*u(1)+u(2)*u(2)+....+u(n)*u(n);
  – HTCom
  Aug 6 at 15:32
  
  

  
  
  
  

How can I formulate objective function in Matlab with undefined number of argument? $u=(u_1, u_2, ..., u_n)$ Just like this objective = @(u) u(1)+u(2)+.......+u(n)+u(1)*u(1)+u(2)*u(2)+....+u(n)*u(n);
– HTCom
Aug 6 at 15:32

How can I formulate objective function in Matlab with undefined number of argument? $u=(u_1, u_2, ..., u_n)$ Just like this objective = @(u) u(1)+u(2)+.......+u(n)+u(1)*u(1)+u(2)*u(2)+....+u(n)*u(n);
– HTCom
Aug 6 at 15:32

add a comment |