Parameters
- C : -
a matrix of double, represents the multiplier of the solution x in the expression C*x - d. C is M-by-N, where M is the number of equations, and N is the number of elements of x.
+ a matrix of double, represents the multiplier of the solution x in the expression C*x - d. Number of columns in C is equal to the number of elements in x.
- d : -
a vector of double, represents the additive constant term in the expression C*x - d. d is M-by-1, where M is the number of equations.
+ a vector of double, represents the additive constant term in the expression C*x - d. Number of elements in d is equal to the number of rows in C matrix.
- A :
a vector of double, represents the linear coefficients in the inequality constraints
- b : @@ -57,9 +57,9 @@
a matrix of double, represents the linear coefficients in the equality constraints
- beq :
a vector of double, represents the linear coefficients in the equality constraints
- - LB :
+
- lb :
a vector of double, contains lower bounds of the variables.
- - UB :
+
- ub :
a vector of double, contains upper bounds of the variables.
- x0 :
a vector of double, contains initial guess of variables.
@@ -72,16 +72,16 @@
- residual :
a vector of double, solution residuals returned as the vector C*x-d.
- exitflag : -
Integer identifying the reason the algorithm terminated.
+ Integer identifying the reason the algorithm terminated. It could be 0, 1 or 2 etc. i.e. Optimal, Maximum Number of Iterations Exceeded, CPU time exceeded. Other flags one can see in the lsqlin macro.
- output : -
Structure containing information about the optimization. Right now it contains number of iteration.
+ Structure containing information about the optimization. This version only contains number of iterations.
- lambda : -
Structure containing the Lagrange multipliers at the solution x (separated by constraint type).It contains lower, upper and linear equality, inequality constraints.
Structure containing the Lagrange multipliers at the solution x (separated by constraint type).It contains lower, upper bound multiplier and linear equality, inequality constraints.
Description
Search the minimum of a constrained linear least square problem specified by :
-
We are calling IPOpt for solving the linear least square problem, IPOpt is a library written in C++.
+
The routine calls Ipopt for solving the linear least square problem, Ipopt is a library written in C++.
Examples
@@ -106,7 +106,7 @@ // Press ENTER to continue
Examples
-//A basic example for equality, inequality and bounds + | | |
Authors
- Keyur Joshi, Saikiran, Iswarya, Harpreet Singh
a matrix of double, represents the linear coefficients in the equality constraints
a vector of double, represents the linear coefficients in the equality constraints
a vector of double, contains lower bounds of the variables.
a vector of double, contains upper bounds of the variables.
a vector of double, contains initial guess of variables.
a double, the function value at x.
Integer identifying the reason the algorithm terminated.
Integer identifying the reason the algorithm terminated.It could be 0, 1 or 2 etc. i.e. Optimal, Maximum Number of Iterations Exceeded, CPU time exceeded. Other flags one can see in the qpipoptmat macro.
Structure containing information about the optimization. Right now it contains number of iteration.
Structure containing information about the optimization. This version only contains number of iterations.
Structure containing the Lagrange multipliers at the solution x (separated by constraint type).It contains lower, upper and linear equality, inequality constraints.
Description
Search the minimum of a constrained linear quadratic optimization problem specified by : find the minimum of f(x) such that
-
We are calling IPOpt for solving the quadratic problem, IPOpt is a library written in C++.
+
The routine calls Ipopt for solving the quadratic problem, Ipopt is a library written in C++.
Examples
diff --git a/help/en_US/scilab_en_US_help/symphony.html b/help/en_US/scilab_en_US_help/symphony.html index 96be830..b81bbb0 100644 --- a/help/en_US/scilab_en_US_help/symphony.html +++ b/help/en_US/scilab_en_US_help/symphony.html @@ -37,9 +37,9 @@Calling Sequence
-xopt = symphony(nbVar,nbCon,objCoef,isInt,LB,UB,conMatrix,conLB,conUB) -xopt = symphony(nbVar,nbCon,objCoef,isInt,LB,UB,conMatrix,conLB,conUB,objSense) -xopt = symphony(nbVar,nbCon,objCoef,isInt,LB,UB,conMatrix,conLB,conUB,objSense,options) +xopt = symphony(nbVar,nbCon,c,isInt,lb,ub,A,conLB,conUB) +xopt = symphony(nbVar,nbCon,c,isInt,lb,ub,A,conLB,conUB,objSense) +xopt = symphony(nbVar,nbCon,c,isInt,lb,ub,A,conLB,conUB,objSense,options) [xopt,fopt,status,output] = symphony( ... )
Parameters
@@ -47,15 +47,15 @@a double, number of variables.
a double, number of constraints.
a vector of double, represents coefficients of the variables in the objective.
a vector of boolean, represents wether a variable is constrained to be an integer.
a vector of double, represents lower bounds of the variables.
a vector of double, represents upper bounds of the variables.
a matrix of double, represents matrix representing the constraint matrix.
a vector of double, represents lower bounds of the constraints.
The sense (maximization/minimization) of the objective. Use 1(sym_minimize ) or -1 (sym_maximize) here.
a a list containing the the parameters to be set.
a list containing the the parameters to be set.
a vector of double, the computed solution of the optimization problem.
a double, the function value at x.
status flag from symphony.
status flag from symphony. 227 is optimal, 228 is Time limit exceeded, 230 is iteration limit exceeded.
The output data structure contains detailed informations about the optimization process. Right now it contains number of iteration.
The output data structure contains detailed information about the optimization process. This version only contains number of iterations
Description
Search the minimum or maximum of a constrained mixed integer linear programming optimization problem specified by : find the minimum or maximum of f(x) such that
-
We are calling SYMPHONY written in C by gateway files for the actual computation.
+
The routine calls SYMPHONY written in C by gateway files for the actual computation.
Examples
//A basic case : // Objective function -objCoef = [350*5,330*3,310*4,280*6,500,450,400,100]'; +c = [350*5,330*3,310*4,280*6,500,450,400,100]'; // Lower Bound of variable lb = repmat(0,8,1); // Upper Bound of variables ub = [repmat(1,4,1);repmat(%inf,4,1)]; // Constraint Matrix -conMatrix = [5,3,4,6,1,1,1,1; +A = [5,3,4,6,1,1,1,1; 5*0.05,3*0.04,4*0.05,6*0.03,0.08,0.07,0.06,0.03; 5*0.03,3*0.03,4*0.04,6*0.04,0.06,0.07,0.08,0.09;] -// Lower Bound of constrains +// Lower Bound of constraints conlb = [ 25; 1.25; 1.25] -// Upper Bound of constrains +// Upper Bound of constraints conub = [ 25; 1.25; 1.25] // Row Matrix for telling symphony that the is integer or not isInt = [repmat(%t,1,4) repmat(%f,1,4)]; xopt = [1 1 0 1 7.25 0 0.25 3.5] fopt = [8495] // Calling Symphony -[x,f,status,output] = symphony(8,3,c,isInt,lb,ub,conMatrix,conlb,conub,1) +[x,f,status,output] = symphony(8,3,c,isInt,lb,ub,A,conlb,conub,1) // Press ENTER to continue | | |
Examples
@@ -116,7 +116,7 @@ find the minimum or maximum of f(x) such that // st sum{j=1,...,n} r(i,j)x(j) <= b(i) i=1,...,m // x(j)=0 or 1 // The function to be maximize i.e. P(j) -p = [ 504 803 667 1103 834 585 811 856 690 832 846 813 868 793 .. +c = [ 504 803 667 1103 834 585 811 856 690 832 846 813 868 793 .. 825 1002 860 615 540 797 616 660 707 866 647 746 1006 608 .. 877 900 573 788 484 853 942 630 591 630 640 1169 932 1034 .. 957 798 669 625 467 1051 552 717 654 388 559 555 1104 783 .. @@ -124,7 +124,7 @@ find the minimum or maximum of f(x) such that 510 671 575 740 510 675 996 636 826 1022 1140 654 909 799 .. 1162 653 814 625 599 476 767 954 906 904 649 873 565 853 1008 632]'; //Constraint Matrix -conMatrix = [ +A = [ //Constraint 1 42 41 523 215 819 551 69 193 582 375 367 478 162 898 .. 550 553 298 577 493 183 260 224 852 394 958 282 402 604 .. @@ -166,15 +166,15 @@ find the minimum or maximum of f(x) such that 483 336 765 637 981 980 202 35 594 689 602 76 767 693 .. 893 160 785 311 417 748 375 362 617 553 474 915 457 261 350 635 ; ]; -nbCon = size(conMatrix,1) -nbVar = size(conMatrix,2) +nbCon = size(A,1) +nbVar = size(A,2) // Lower Bound of variables lb = repmat(0,nbVar,1) // Upper Bound of variables ub = repmat(1,nbVar,1) // Row Matrix for telling symphony that the is integer or not isInt = repmat(%t,1,nbVar) -// Lower Bound of constrains +// Lower Bound of constraints conLB=repmat(0,nbCon,1); // Upper Bound of constraints conUB=[11927 13727 11551 13056 13460 ]'; @@ -187,7 +187,7 @@ find the minimum or maximum of f(x) such that // Optimal value fopt = [ 24381 ] // Calling Symphony -[x,f,status,output] = symphony(nbVar,nbCon,p,isInt,lb,ub,conMatrix,conLB,conUB,-1,options);Authors
- Keyur Joshi, Saikiran, Iswarya, Harpreet Singh
- - -
fmincon
Solves a nonlinearily constrained optimization problem.
Calling Sequence
-x = fmincon(fun,x0) -x = fmincon(fun,x0,A,b) -x = fmincon(fun,x0,A,b,Aeq,beq) -x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub) -x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon) -x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options) -[x,fval,exitflag,output,lambda,grad,hessian] = fmincon ( ... )
Parameters
-- fun: -
a function, the function to minimize. See below for the complete specifications.
- - x0: -
a nx1 or 1xn matrix of doubles, where n is the number of variables. The initial guess for the optimization algorithm.
- - A: -
a nil x n matrix of doubles, where n is the number of variables and nil is the number of linear inequalities. If A==[] and b==[], it is assumed that there is no linear inequality constraints. If (A==[] & b<>[]), fmincon generates an error (the same happens if (A<>[] & b==[])).
- - b: -
a nil x 1 matrix of doubles, where nil is the number of linear inequalities.
- - Aeq: -
a nel x n matrix of doubles, where n is the number of variables and nel is the number of linear equalities. If A==[] and b==[], it is assumed that there is no linear equality constraints. If (Aeq==[] & beq<>[]), fmincon generates an error (the same happens if (Aeq<>[] & beq==[])).
- - beq: -
a nel x 1 matrix of doubles, where nel is the number of linear inequalities.
- - lb: -
a nx1 or 1xn matrix of doubles, where n is the number of variables. The lower bound for x. If lb==[], then the lower bound is automatically set to -inf.
- - ub: -
a nx1 or 1xn matrix of doubles, where n is the number of variables. The upper bound for x. If lb==[], then the upper bound is automatically set to +inf.
- - nonlcon: -
a function, the nonlinear constraints. See below for the complete specifications.
- - x: -
a nx1 matrix of doubles, the computed solution of the optimization problem
- - fval: -
a 1x1 matrix of doubles, the function value at x
- - exitflag: -
a 1x1 matrix of floating point integers, the exit status. See below for details.
- - output: -
a struct, the details of the optimization process. See below for details.
- - lambda: -
a struct, the Lagrange multipliers at optimum. See below for details.
- - grad: -
a nx1 matrix of doubles, the gradient of the objective function at optimum
- - hessian: -
a nxn matrix of doubles, the Hessian of the objective function at optimum
- - options: -
an optional struct, as provided by optimset
Description
-Search the minimum of a constrained optimization problem specified by : -find the minimum of f(x) such that
-c(x)<=0, ceq(x)<=0, A*x<=b, Aeq*x=beq and lb<=x<=ub.
-
Currently, we use ipopt for the actual solver of fmincon.
-See the demonstrations for additionnal examples.
-The objective function must have header : -
f = objfun ( x ) | | |
By default, fmincon uses finite differences with order 2 formulas and -optimum step size in order to compute a numerical gradient of the -objective function. -If we can provide exact gradients, we should do so since it improves -the convergence speed of the optimization algorithm. -In order to use exact gradients, we must update the header of the -objective function to : -
[f,G] = objfungrad ( x ) | | |
options = optimset("GradObj","on"); | | |
The constraint function must have header : -
[c, ceq] = confun(x) | | |
By default, fmincon uses finite differences with order 2 formulas and -optimum step size in order to compute a numerical gradient of the -constraint function. -In order to use exact gradients, we must update the header of the -constraint function to : -
[c,ceq,DC,DCeq] = confungrad(x) | | |
options = optimset("GradConstr","on"); | | |
By default, fmincon uses a L-BFGS formula to compute an -approximation of the Hessian of the Lagrangian. -Notice that this is different from Matlab's fmincon, which -default is to use a BFGS.
-The exitflag variable allows to know the status of the optimization. -
- exitflag=0 : Number of iterations exceeded options.MaxIter or number of function evaluations exceeded options.FunEvals. -
- exitflag=1 : First-order optimality measure was less than options.TolFun, and maximum constraint violation was less than options.TolCon. -
- exitflag=-1 : The output function terminated the algorithm. -
- exitflag=-2 : No feasible point was found. -
- exitflag=%nan : Other type of termination.
The output data structure contains detailed informations about the -optimization process. -It has type "struct" and contains the following fields. -
- output.iterations: the number of iterations performed during the search -
- output.funcCount: the number of function evaluations during the search -
- output.stepsize: an empty matrix -
- output.algorithm : the string containing the name of the algorithm. In the current version, algorithm="ipopt". -
- output.firstorderopt: the max-norm of the first-order KKT conditions. -
- output.constrviolation: the max-norm of the constraint violation. -
- output.cgiterations: the number of preconditionned conjugate gradient steps. In the current version, cgiterations=0. -
- output.message: a string containing a message describing the status of the optimization.
The lambda data structure contains the Lagrange multipliers at the -end of optimization. -It has type "struct" and contains the following -fields. -
- lambda.lower: the Lagrange multipliers for the lower bound constraints. In the current version, an empty matrix. -
- lambda.upper: the Lagrange multipliers for the upper bound constraints. In the current version, an empty matrix. -
- lambda.eqlin: the Lagrange multipliers for the linear equality constraints. -
- lambda.eqnonlin: the Lagrange multipliers for the nonlinear equality constraints. -
- lambda.ineqlin: the Lagrange multipliers for the linear inequality constraints. -
- lambda.ineqnonlin: the Lagrange multipliers for the nonlinear inequality constraints.
TODO : exitflag=2 : Change in x was less than options.TolX and maximum constraint violation was less than options.TolCon. -TODO : exitflag=-3 : Current point x went below options.ObjectiveLimit and maximum constraint violation was less than options.TolCon. -TODO : fill lambda.lower and lambda.upper consistently. See ticket #111 : http://forge.scilab.org/index.php/p/sci-ipopt/issues/111/ -TODO : test with A, b -TODO : test with Aeq, beq -TODO : test with ceq -TODO : avoid using global for ipopt_data -TODO : implement Display option -TODO : implement FinDiffType option -TODO : implement MaxFunEvals option -TODO : implement DerivativeCheck option -TODO : implement MaxIter option -TODO : implement OutputFcn option -TODO : implement PlotFcns option -TODO : implement TolFun option -TODO : implement TolCon option -TODO : implement TolX option -TODO : implement Hessian option -TODO : check that the hessian output argument is Hessian of f only -TODO : test all exitflag values
-Examples
-// A basic case : -// we provide only the objective function and the nonlinear constraint -// function : we let fmincon compute the gradients by numerical -// derivatives. -function f=objfun(x) -f = exp(x(1))*(4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1) -endfunction -function [c, ceq]=confun(x) -// Nonlinear inequality constraints -c = [ -1.5 + x(1)*x(2) - x(1) - x(2) --x(1)*x(2) - 10 -] -// Nonlinear equality constraints -ceq = [] -endfunction -// The initial guess -x0 = [-1,1]; -// The expected solution : only 4 digits are guaranteed -xopt = [-9.547345885974547 1.047408305349257] -fopt = 0.023551460139148 -// Run fmincon -[x,fval,exitflag,output,lambda,grad,hessian] = .. -fmincon ( objfun,x0,[],[],[],[],[],[], confun ) | | |
Examples
-// A case where we provide the gradient of the objective -// function and the Jacobian matrix of the constraints. -// The objective function and its gradient -function [f, G]=objfungrad(x) -[lhs,rhs]=argn() -f = exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1) -if ( lhs > 1 ) then -G = [ -f + exp(x(1)) * (8*x(1) + 4*x(2)) -exp(x(1))*(4*x(1)+4*x(2)+2) -] -end -endfunction -// The nonlinear constraints and the Jacobian -// matrix of the constraints -function [c, ceq, DC, DCeq]=confungrad(x) -// Inequality constraints -c(1) = 1.5 + x(1) * x(2) - x(1) - x(2) -c(2) = -x(1) * x(2)-10 -// No nonlinear equality constraints -ceq=[] -[lhs,rhs]=argn() -if ( lhs > 2 ) then -// DC(:,i) = gradient of the i-th constraint -// DC = [ -// Dc1/Dx1 Dc2/Dx1 -// Dc1/Dx2 Dc2/Dx2 -// ] -DC= [ -x(2)-1, -x(2) -x(1)-1, -x(1) -] -DCeq = [] -end -endfunction -// Test with both gradient of objective and gradient of constraints -options = optimset("GradObj","on","GradConstr","on"); -// The initial guess -x0 = [-1,1]; -// The expected solution : only 4 digits are guaranteed -xopt = [-9.547345885974547 1.047408305349257] -fopt = 0.023551460139148 -// Run fmincon -[x,fval,exitflag,output] = .. -fmincon(objfungrad,x0,[],[],[],[],[],[], confungrad,options) | | |
Examples
-// A case where we set the bounds of the optimization. -// By default, the bounds are set to infinity. -function f=objfun(x) -f = exp(x(1))*(4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1) -endfunction -function [c, ceq]=confun(x) -// Nonlinear inequality constraints -c = [ -1.5 + x(1)*x(2) - x(1) - x(2) --x(1)*x(2) - 10 -] -// Nonlinear equality constraints -ceq = [] -endfunction -// The initial guess -x0 = [-1,1]; -// The expected solution -xopt = [0 1.5] -fopt = 8.5 -// Make sure that x(1)>=0, and x(2)>=0 -lb = [0,0]; -ub = [ ]; -// Run fmincon -[x,fval] = fmincon ( objfun , x0,[],[],[],[],lb,ub,confun) | | |
Authors
-- Michael Baudin, DIGITEO, 2010
- - - - diff --git a/help/en_US/scilab_en_US_help/symphonymat.html b/help/en_US/scilab_en_US_help/symphonymat.html index c580508..fc60daf 100644 --- a/help/en_US/scilab_en_US_help/symphonymat.html +++ b/help/en_US/scilab_en_US_help/symphonymat.html @@ -37,25 +37,25 @@
Calling Sequence
-xopt = symphonymat(C,intcon,A,b) -xopt = symphonymat(C,intcon,A,b,Aeq,beq) -xopt = symphonymat(C,intcon,A,b,Aeq,beq,lb,ub) -xopt = symphonymat(C,intcon,A,b,Aeq,beq,lb,ub,options) +xopt = symphonymat(c,intcon,A,b) +xopt = symphonymat(c,intcon,A,b,Aeq,beq) +xopt = symphonymat(c,intcon,A,b,Aeq,beq,lb,ub) +xopt = symphonymat(c,intcon,A,b,Aeq,beq,lb,ub,options) [xopt,fopt,status,output] = symphonymat( ... )
Parameters
-- f : +
- c :
a vector of double, contains coefficients of the variables in the objective
- intcon :
Vector of integer constraints, specified as a vector of positive integers. The values in intcon indicate the components of the decision variable x that are integer-valued. intcon has values from 1 through number of variable.
- A : -
Linear inequality constraint matrix, specified as a matrix of double. A represents the linear coefficients in the constraints A*x ≤ b. A has size M-by-N, where M is the number of constraints and N is number of variables
+ Linear inequality constraint matrix, specified as a matrix of double. A represents the linear coefficients in the constraints A*x ≤ b. A has the size where columns equals to the number of variables.
- b : -
Linear inequality constraint vector, specified as a vector of double. b represents the constant vector in the constraints A*x ≤ b. b has length M, where A is M-by-N
+ Linear inequality constraint vector, specified as a vector of double. b represents the constant vector in the constraints A*x ≤ b. b has size equals to the number of rows in A.
- Aeq : -
Linear equality constraint matrix, specified as a matrix of double. Aeq represents the linear coefficients in the constraints Aeq*x = beq. Aeq has size Meq-by-N, where Meq is the number of constraints and N is number of variables
+ Linear equality constraint matrix, specified as a matrix of double. Aeq represents the linear coefficients in the constraints Aeq*x = beq. Aeq has the size where columns equals to the number of variables.
- beq : -
Linear equality constraint vector, specified as a vector of double. beq represents the constant vector in the constraints Aeq*x = beq. beq has length Meq, where Aeq is Meq-by-N.
+ Linear equality constraint vector, specified as a vector of double. beq represents the constant vector in the constraints Aeq*x = beq. beq has size equals to the number of rows in Aeq.
- lb :
Lower bounds, specified as a vector or array of double. lb represents the lower bounds elementwise in lb ≤ x ≤ ub.
- ub :
@@ -63,24 +63,24 @@
- options :
a list containing the the parameters to be set.
- xopt : -
a vector of double, the computed solution of the optimization problem
+ a vector of double, the computed solution of the optimization problem.
- fopt :
a double, the function value at x
- status : -
status flag from symphony.
+ status flag from symphony. 227 is optimal, 228 is Time limit exceeded, 230 is iteration limit exceeded.
- output : -
The output data structure contains detailed informations about the optimization process. Right now it contains number of iteration.
The output data structure contains detailed information about the optimization process. This version only contains number of iterations.
Description
Search the minimum or maximum of a constrained mixed integer linear programming optimization problem specified by : -find the minimum or maximum of f(x) such that
-
We are calling SYMPHONY written in C by gateway files for the actual computation.
+find the minimum or maximum of C'⋅x such that +
The routine calls SYMPHONY written in C by gateway files for the actual computation.
Examples
// Objective function -C = [350*5,330*3,310*4,280*6,500,450,400,100]'; +c = [350*5,330*3,310*4,280*6,500,450,400,100]'; // Lower Bound of variable lb = repmat(0,1,8); // Upper Bound of variables @@ -106,7 +106,7 @@ find the minimum or maximum of f(x) such that // st sum{j=1,...,n} r(i,j)x(j) <= b(i) i=1,...,m // x(j)=0 or 1 // The function to be maximize i.e. P(j) -C = -1*[ 504 803 667 1103 834 585 811 856 690 832 846 813 868 793 .. +c = -1*[ 504 803 667 1103 834 585 811 856 690 832 846 813 868 793 .. 825 1002 860 615 540 797 616 660 707 866 647 746 1006 608 .. 877 900 573 788 484 853 942 630 591 630 640 1169 932 1034 .. 957 798 669 625 467 1051 552 717 654 388 559 555 1104 783 .. @@ -155,7 +155,7 @@ find the minimum or maximum of f(x) such that 483 336 765 637 981 980 202 35 594 689 602 76 767 693 .. 893 160 785 311 417 748 375 362 617 553 474 915 457 261 350 635 ; ]; -nbVar = size(objCoef,1) +nbVar = size(c,1) b=[11927 13727 11551 13056 13460 ]; // Lower Bound of variables lb = repmat(0,1,nbVar) @@ -175,7 +175,7 @@ find the minimum or maximum of f(x) such that // Optimal value fopt = [ 24381 ] // Calling Symphony -[x,f,status,output] = symphonymat(C,intcon,A,b,[],[],lb,ub,options); | | |
Authors
- Keyur Joshi, Saikiran, Iswarya, Harpreet Singh