qps_ipopt
- qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt)
qps_ipopt()- Quadratic Program Solver based on IPOPT.[X, F, EXITFLAG, OUTPUT, LAMBDA] = ... QPS_IPOPT(H, C, A, L, U, XMIN, XMAX, X0, OPT) [X, F, EXITFLAG, OUTPUT, LAMBDA] = QPS_IPOPT(PROBLEM) A wrapper function providing a standardized interface for using IPOPT 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 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 ipopt_opt - options struct for IPOPT, 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, opt Outputs: X : solution vector F : final objective function value EXITFLAG : exit flag 1 = converged 0 = failed to converge OUTPUT : output struct with the following fields: status - see IPOPT documentation for INFO.status https://coin-or.github.io/Ipopt/IpReturnCodes__inc_8h_source.html iterations - number of iterations performed (INFO.iter) cpu - see IPOPT documentation for INFO.cpu eval - see IPOPT documentation for INFO.eval 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] = ... qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt) x = qps_ipopt(H, c, A, l, u) x = qps_ipopt(H, c, A, l, u, xmin, xmax) x = qps_ipopt(H, c, A, l, u, xmin, xmax, x0) x = qps_ipopt(H, c, A, l, u, xmin, xmax, x0, opt) x = qps_ipopt(problem), where problem is a struct with fields: H, c, A, l, u, xmin, xmax, x0, opt all fields except 'c', 'A' and 'l' or 'u' are optional x = qps_ipopt(...) [x, f] = qps_ipopt(...) [x, f, exitflag] = qps_ipopt(...) [x, f, exitflag, output] = qps_ipopt(...) [x, f, exitflag, output, lambda] = qps_ipopt(...) 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] = qps_ipopt(H, c, A, l, u, xmin, [], x0, opt);
See https://github.com/coin-or/Ipopt.
See also
qps_master(),ipopt,ipopt_options().