symphony_mat Solves a mixed integer linear programming constrained optimization problem. xopt = symphony_mat(f,intcon,A,b) xopt = symphony_mat(f,intcon,A,b,Aeq,beq) xopt = symphony_mat(f,intcon,A,b,Aeq,beq,lb,ub) xopt = symphony_mat(f,intcon,A,b,Aeq,beq,lb,ub,options) [xopt,fopt,iter] = symphony_mat( ... ) f : a 1xn matrix of doubles, where n is number of variables, 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 doubles. 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 b : Linear inequality constraint vector, specified as a vector of doubles. b represents the constant vector in the constraints A*x ≤ b. b has length M, where A is M-by-N Aeq : Linear equality constraint matrix, specified as a matrix of doubles. 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 beq : Linear equality constraint vector, specified as a vector of doubles. beq represents the constant vector in the constraints Aeq*x = beq. beq has length Meq, where Aeq is Meq-by-N. lb : Lower bounds, specified as a vector or array of doubles. lb represents the lower bounds elementwise in lb ≤ x ≤ ub. ub : Upper bounds, specified as a vector or array of doubles. ub represents the upper bounds elementwise in lb ≤ x ≤ ub. options : a 1xq marix of string, provided to set the paramters in symphony xopt : a 1xn matrix of doubles, the computed solution of the optimization problem fopt : a 1x1 matrix of doubles, the function value at x iter : a 1x1 matrix of doubles, contains the number od iterations done by symphony 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 \begin{eqnarray} \mbox{min}_{x} & f(x) \\ \mbox{subject to} & c(x) \leq 0 \\ & c_{eq}(x) = 0 \\ & Ax \leq b \\ & A_{eq} x = b_{eq} \\ & lb \leq x \leq ub \end{eqnarray} Keyur Joshi, Saikiran, Iswarya, Harpreet Singh