From 6aa3bf99dbd4187c83167dec18ebe974421d57bc Mon Sep 17 00:00:00 2001 From: Georgey Date: Wed, 5 Jul 2017 11:44:38 +0530 Subject: Updated help folder --- help/en_US/scilab_en_US_help/intqpipopt.html | 267 +++++++++++++++++++++++++++ 1 file changed, 267 insertions(+) create mode 100644 help/en_US/scilab_en_US_help/intqpipopt.html (limited to 'help/en_US/scilab_en_US_help/intqpipopt.html') diff --git a/help/en_US/scilab_en_US_help/intqpipopt.html b/help/en_US/scilab_en_US_help/intqpipopt.html new file mode 100644 index 0000000..2fbad90 --- /dev/null +++ b/help/en_US/scilab_en_US_help/intqpipopt.html @@ -0,0 +1,267 @@ + + + intqpipopt + + + +
+ + + + +
+ << intfminunc + + + FOSSEE Optimization Toolbox + + + linprog >> + +
+
+
+ + + + FOSSEE Optimization Toolbox >> FOSSEE Optimization Toolbox > intqpipopt + +

+

intqpipopt

+

Solves a linear quadratic problem.

+ + +

Calling Sequence

+ 
xopt = intqpipopt(H,f)
+xopt = intqpipopt(H,f,intcon)
+xopt = intqpipopt(H,f,intcon,A,b)
+xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq)
+xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub)
+xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub,x0)
+xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub,x0,options)
+xopt = intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub,x0,options,"file_path")
+[xopt,fopt,exitflag,output] = intqpipopt( ... )
+ +

Input Parameters

+
H : +

A symmetric matrix of doubles, representing the Hessian of the quadratic problem.

+
f : +

A vector of doubles, representing coefficients of the linear terms in the quadratic problem.

+
intcon : +

A vector of integers, representing the variables that are constrained to be integers.

+
A : +

A matrix of doubles, containing the coefficients of linear inequality constraints of size (m X n) where 'm' is the number of linear inequality constraints.

+
b : +

A vector of doubles, related to 'A' and represents the linear coefficients in the linear inequality constraints of size (m X 1).

+
Aeq : +

A matrix of doubles, containing the coefficients of linear equality constraints of size (m1 X n) where 'm1' is the number of linear equality constraints.

+
beq : +

A vector of double, vector of doubles, related to 'Aeq' and represents the linear coefficients in the equality constraints of size (m1 X 1).

+
lb : +

A vector of doubles, containing the lower bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of variables.

+
ub : +

A vector of doubles, containing the upper bounds of the variables of size (1 X n) or (n X 1) where 'n' is the number of variables.

+
x0 : +

A vector of doubles, containing the starting values of variables of size (1 X n) or (n X 1) where 'n' is the number of variables.

+
options : +

A list, containing the option for user to specify. See below for details.

+
file_path : +

path to bonmin opt file if used.

+

Outputs

+
xopt : +

A vector of doubles, containing the computed solution of the optimization problem.

+
fopt : +

A double, containing the value of the function at xopt.

+
exitflag : +

An integer, containing the flag which denotes the reason for termination of algorithm. See below for details.

+
output : +

A structure, containing the information about the optimization. See below for details.

+ +

Description

+

Search the minimum of a constrained linear quadratic optimization problem specified by :

+

+

intqpipopt calls Bonmin, a library written in C++ to solve the quadratic problem.

+

The exitflag allows to know the status of the optimization which is given back by Ipopt. +

+

For more details on exitflag, see the Bonmin documentation which can be found on http://www.coin-or.org/Bonmin

+

+

The output data structure contains detailed information about the optimization process. +It is of type "struct" and contains the following fields. +

+

+

A few examples displaying the various functionalities of intqpipopt have been provided below. You will find a series of problems and the appropriate code snippets to solve them.

+

Example

+

Here we solve a simple objective function.

+

Find x in R^6 such that it minimizes:

+

+

+ 
//Example 1:
+//Minimize 0.5*x'*H*x + f'*x with
+f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
+//Integer Constraints
+intcon = [2 ,4];
+//Running intqpipopt
+[xopt,fopt,exitflag,output,lambda]=qpipoptmat(H,f)
+ +

Example

+ We proceed to add simple linear inequality constraints. + +

+

+ 
//Example 2:
+f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
+//Inequality constraints
+A= [0,1,0,1,2,-1;
+-1,0,2,1,1,0];
+b = [-1; 2.5];
+//Integer Constraints
+intcon = [2 ,4];
+//Running intqpipopt
+[xopt,fopt,exitflag,output,lambda]=intqpipopt(H,f,intcon,A,b)
+ +

Example

+ Here we build up on the previous example by adding linear equality constraints. +We add the following constraints to the problem specified above: +

+

+ 
//Example 3:
+//Minimize 0.5*x'*H*x + f'*x with
+f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
+//Inequality constraints
+A= [0,1,0,1,2,-1;
+-1,0,2,1,1,0];
+b = [-1; 2.5];
+//Equality constraints
+Aeq= [1,-1,1,0,3,1;
+-1,0,-3,-4,5,6;
+2,5,3,0,1,0];
+beq=[1; 2; 3];
+//Integer Constraints
+intcon = [2 ,4];
+//Running intqpipopt
+[xopt,fopt,exitflag,output,lambda]=intqpipopt(H,f,intcon,A,b,Aeq,beq)
+ +

Example

+

In this example, we proceed to add the upper and lower bounds to the objective function.

+

+

+ 
//Example 4:
+//Minimize 0.5*x'*H*x + f'*x with
+f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
+//Inequality constraints
+A= [0,1,0,1,2,-1;
+-1,0,2,1,1,0];
+b = [-1; 2.5];
+//Equality constraints
+Aeq= [1,-1,1,0,3,1;
+-1,0,-3,-4,5,6;
+2,5,3,0,1,0];
+beq=[1; 2; 3];
+//Variable bounds
+lb=[-1000; -10000; 0; -1000; -1000; -1000];
+ub=[10000; 100; 1.5; 100; 100; 1000];
+//Integer Constraints
+intcon = [2 ,4];
+//Running intqpipopt
+[xopt,fopt,exitflag,output,lambda]=intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub)
+ +

Example

+

In this example, we initialize the values of x to speed up the computation. We further enhance the functionality of qpipoptmat by setting input options.

+ 
//Example 5:
+//Minimize 0.5*x'*H*x + f'*x with
+f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
+//Inequality constraints
+A= [0,1,0,1,2,-1;
+-1,0,2,1,1,0];
+b = [-1; 2.5];
+//Equality constraints
+Aeq= [1,-1,1,0,3,1;
+-1,0,-3,-4,5,6;
+2,5,3,0,1,0];
+beq=[1; 2; 3];
+//Variable bounds
+lb=[-1000; -10000; 0; -1000; -1000; -1000];
+ub=[10000; 100; 1.5; 100; 100; 1000];
+//Initial guess and options
+x0 = repmat(0,6,1);
+options = list("MaxIter", 300, "CpuTime", 100);
+//Integer Constraints
+intcon = [2 ,4];
+//Running intqpipopt
+[xopt,fopt,exitflag,output,lambda]=intqpipopt(H,f,intcon,A,b,Aeq,beq,lb,ub,x0,options)
+ +

Example

+Infeasible Problems: Find x in R^6 such that it minimizes the objective function used above under the following constraints: +

+

+
//Example 6:
+//Minimize 0.5*x'*H*x + f'*x with
+f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
+f=[1; 2; 3; 4; 5; 6]; H=eye(6,6);
+//Inequality constraints
+A= [0,1,0,1,2,-1;
+-1,0,2,1,1,0];
+b = [-1; 2.5];
+//Equality constraints
+Aeq= [0,1,0,1,2,-1;
+-1,0,-3,-4,5,6];
+beq=[4; 2];
+//Integer Constraints
+intcon = [2 ,4];
+//Running intqpipopt
+[xopt,fopt,exitflag,output,lambda]=intqpipopt(H,f,intcon,A,b,Aeq,beq)
+ +

Example

+

Unbounded Problems: Find x in R^6 such that it minimizes the objective function used above under the following constraints:

+

+

+ 
//Example 7:
+//Minimize 0.5*x'*H*x + f'*x with
+f=[1; 2; 3; 4; 5; 6]; H=eye(6,6); H(1,1) = -1;
+//Inequality constraints
+A= [0,1,0,1,2,-1;
+-1,0,2,1,1,0];
+b = [-1; 2.5];
+//Equality constraints
+Aeq= [1,-1,1,0,3,1;
+-1,0,-3,-4,5,6];
+beq=[1; 2];
+intcon = [2 ,4];
+//Running intqpipopt
+[xopt,fopt,exitflag,output,lambda]=intqpipopt(H,f,intcon,A,b,Aeq,beq)
+ +

Authors

+
+
+ +
+ + + + + + +
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