miqps_ot
- miqps_ot(H, c, A, l, u, xmin, xmax, x0, vtype, opt)
miqps_ot()- Mixed Integer Linear Program Solver based on INTLINPROG.[X, F, EXITFLAG, OUTPUT, LAMBDA] = ... MIQPS_OT(H, C, A, L, U, XMIN, XMAX, X0, VTYPE, OPT) [X, F, EXITFLAG, OUTPUT, LAMBDA] = MIQPS_OT(PROBLEM) A wrapper function providing a standardized interface for using QUADPROG or LINPROG from the Optimization Toolbox to solve the following QP (quadratic programming) problem: min 1/2 X'*H*X + C'*X X subject to L <= A*X <= U (linear constraints) XMIN <= X <= XMAX (variable bounds) Inputs (all optional except H, C, A and L): H : matrix (possibly sparse) of quadratic cost coefficients C : vector of linear cost coefficients A, L, U : define the optional linear constraints. Default values for the elements of L and U are -Inf and Inf, respectively. XMIN, XMAX : optional lower and upper bounds on the X variables, defaults are -Inf and Inf, respectively. X0 : optional starting value of optimization vector X VTYPE : character string of length NX (number of elements in X), or 1 (value applies to all variables in x), allowed values are 'C' (continuous), 'B' (binary) or 'I' (integer). OPT : optional options structure with the following fields, all of which are also optional (default values shown in parentheses) verbose (0) - controls level of progress output displayed 0 = no progress output 1 = some progress output 2 = verbose progress output skip_prices (0) - flag that specifies whether or not to skip the price computation stage, in which the problem is re-solved for only the continuous variables, with all others being constrained to their solved values price_stage_warn_tol (1e-7) - tolerance on the objective fcn value and primal variable relative match required to avoid mis-match warning message intlinprog_opt - options struct for INTLINPROG, value in verbose overrides these options linprog_opt - options struct for LINPROG, value in verbose overrides these options PROBLEM : The inputs can alternatively be supplied in a single PROBLEM struct with fields corresponding to the input arguments described above: H, c, A, l, u, xmin, xmax, x0, vtype, opt Outputs: X : solution vector F : final objective function value EXITFLAG : QUADPROG/LINPROG exit flag (see QUADPROG and LINPROG documentation for details) OUTPUT : QUADPROG/LINPROG output struct (see QUADPROG and LINPROG documentation for details) LAMBDA : struct containing the Langrange and Kuhn-Tucker multipliers on the constraints, with fields: mu_l - lower (left-hand) limit on linear constraints mu_u - upper (right-hand) limit on linear constraints lower - lower bound on optimization variables upper - upper bound on optimization variables Note the calling syntax is almost identical to that of QUADPROG from MathWorks' Optimization Toolbox. The main difference is that the linear constraints are specified with A, L, U instead of A, B, Aeq, Beq. Calling syntax options: [x, f, exitflag, output, lambda] = ... miqps_ot(H, c, A, l, u, xmin, xmax, x0, vtype, opt) x = miqps_ot(H, c, A, l, u) x = miqps_ot(H, c, A, l, u, xmin, xmax) x = miqps_ot(H, c, A, l, u, xmin, xmax, x0) x = miqps_ot(H, c, A, l, u, xmin, xmax, x0, vtype) x = miqps_ot(H, c, A, l, u, xmin, xmax, x0, vtype, opt) x = miqps_ot(problem), where problem is a struct with fields: H, c, A, l, u, xmin, xmax, x0, vtype, opt all fields except 'c', 'A' and 'l' or 'u' are optional x = miqps_ot(...) [x, f] = miqps_ot(...) [x, f, exitflag] = miqps_ot(...) [x, f, exitflag, output] = miqps_ot(...) [x, f, exitflag, output, lambda] = miqps_ot(...) Example: (problem from from https://v8doc.sas.com/sashtml/iml/chap8/sect12.htm) H = [ 1003.1 4.3 6.3 5.9; 4.3 2.2 2.1 3.9; 6.3 2.1 3.5 4.8; 5.9 3.9 4.8 10 ]; c = zeros(4,1); A = [ 1 1 1 1; 0.17 0.11 0.10 0.18 ]; l = [1; 0.10]; u = [1; Inf]; xmin = zeros(4,1); x0 = [1; 0; 0; 1]; opt = struct('verbose', 2); [x, f, s, out, lambda] = miqps_ot(H, c, A, l, u, xmin, [], x0, vtype, opt);
See also
miqps_master(),intlinprog,quadprog,linprog.