intfmincon Solves a constrainted multi-variable mixed integer non linear programming problem xopt = intfmincon(f,x0,intcon,A,b) xopt = intfmincon(f,x0,intcon,A,b,Aeq,beq) xopt = intfmincon(f,x0,intcon,A,b,Aeq,beq,lb,ub) xopt = intfmincon(f,x0,intcon,A,b,Aeq,beq,lb,ub,nlc) xopt = intfmincon(f,x0,intcon,A,b,Aeq,beq,lb,ub,nlc,options) [xopt,fopt] = intfmincon(.....) [xopt,fopt,exitflag]= intfmincon(.....) [xopt,fopt,exitflag,gradient]=intfmincon(.....) [xopt,fopt,exitflag,gradient,hessian]=intfmincon(.....) f : a function, representing the objective function of the problem x0 : a vector of doubles, containing the starting values of variables. intcon : a vector of integers, represents which variables are constrained to be integers A : a matrix of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b. b : a vector of double, represents the linear coefficients in the inequality constraints A⋅x ≤ b. Aeq : a matrix of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq. beq : a vector of double, represents the linear coefficients in the equality constraints Aeq⋅x = beq. lb : Lower bounds, specified as a vector or array of double. lb represents the lower bounds elementwise in lb ≤ x ≤ ub. ub : Upper bounds, specified as a vector or array of double. ub represents the upper bounds elementwise in lb ≤ x ≤ ub. nlc : a function, representing the Non-linear Constraints functions(both Equality and Inequality) of the problem. It is declared in such a way that non-linear inequality constraints are defined first as a single row vector (c), followed by non-linear equality constraints as another single row vector (ceq). Refer Example for definition of Constraint function. options : a list, containing the option for user to specify. See below for details. xopt : a vector of doubles, containing the the computed solution of the optimization problem. fopt : a scalar of double, containing the the function value at x. exitflag : a scalar of integer, containing the flag which denotes the reason for termination of algorithm. See below for details. gradient : a vector of doubles, containing the Objective's gradient of the solution. hessian : a matrix of doubles, containing the Objective's hessian of the solution. Search the minimum of a mixed integer constrained optimization problem specified by : Find the minimum of f(x) such that \begin{eqnarray} &\mbox{min}_{x} & f(x) \\ & \text{subject to} & A*x \leq b \\ & & Aeq*x \ = beq\\ & & c(x) \leq 0\\ & & ceq(x) \ = 0\\ & & lb \leq x \leq ub \\ & & x_i \in \!\, \mathbb{Z}, i \in \!\, I \end{eqnarray} The routine calls Bonmin for solving the Bounded Optimization problem, Bonmin is a library written in C++. The options allows the user to set various parameters of the Optimization problem. It should be defined as type "list" and contains the following fields. Syntax : options= list("IntegerTolerance", [---], "MaxNodes",[---], "MaxIter", [---], "AllowableGap",[---] "CpuTime", [---],"gradobj", "off", "hessian", "off" ); IntegerTolerance : a Scalar, a number with that value of an integer is considered integer.. MaxNodes : a Scalar, containing the Maximum Number of Nodes that the solver should search. CpuTime : a Scalar, containing the Maximum amount of CPU Time that the solver should take. AllowableGap : a Scalar, to stop the tree search when the gap between the objective value of the best known solution is reached. MaxIter : a Scalar, containing the Maximum Number of Iteration that the solver should take. gradobj : a string, to turn on or off the user supplied objective gradient. hessian : a Scalar, to turn on or off the user supplied objective hessian. Default Values : options = list('integertolerance',1d-06,'maxnodes',2147483647,'cputime',1d10,'allowablegap',0,'maxiter',2147483647,'gradobj',"off",'hessian',"off") The exitflag allows to know the status of the optimization which is given back by Ipopt. exitflag=0 : Optimal Solution Found exitflag=1 : InFeasible Solution. exitflag=2 : Objective Function is Continuous Unbounded. exitflag=3 : Limit Exceeded. exitflag=4 : User Interrupt. exitflag=5 : MINLP Error. For more details on exitflag see the Bonmin documentation, go to http://www.coin-or.org/Bonmin Harpreet Singh