[X, F, EXITFLAG, OUTPUT, LAMBDA] = ...
QPS_MASTER(H, C, A, L, U, XMIN, XMAX, X0, OPT)
[X, F, EXITFLAG, OUTPUT, LAMBDA] = QPS_MASTER(PROBLEM)
A common wrapper function for various QP solvers.
Solves 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)
alg ('DEFAULT') : determines which solver to use, can be either
a string (new-style) or a numerical alg code (old-style)
'DEFAULT' : (or 0) automatic, first available of Gurobi,
CPLEX, MOSEK, Opt Tbx (if MATLAB), GLPK (LPs only),
BPMPD, MIPS
'MIPS' : (or 200) MIPS, MATPOWER Interior Point Solver
pure MATLAB implementation of a primal-dual
interior point method, if mips_opt.step_control = 1
(or alg=250) it uses MIPS-sc, a step controlled
variant of MIPS
'BPMPD' : (or 100) BPMPD_MEX
'CLP' : CLP
'CPLEX' : (or 500) CPLEX
'GLPK' : GLPK, (LP problems only, i.e. empty H matrix)
'GUROBI' : (or 700) Gurobi
'IPOPT' : (or 400) IPOPT, requires MEX interface to IPOPT
solver, https://github.com/coin-or/Ipopt
'MOSEK' : (or 600) MOSEK
'OSQP' : OSQP, https://osqp.org
'OT' : (or 300) Optimization Toolbox, QUADPROG or LINPROG
verbose (0) - controls level of progress output displayed
0 = no progress output
1 = some progress output
2 = verbose progress output
bp_opt - options vector for BP
clp_opt - options vector for CLP
cplex_opt - options struct for CPLEX
glpk_opt - options struct for GLPK
grb_opt - options struct for GUROBI
ipopt_opt - options struct for IPOPT
linprog_opt - options struct for LINPROG
mips_opt - options struct for QPS_MIPS
mosek_opt - options struct for MOSEK
osqp_opt - options struct for OSQP
quadprog_opt - options struct for QUADPROG
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 or negative values = solver specific failure codes
OUTPUT : output struct with the following fields:
alg - algorithm code of solver used
(others) - algorithm specific fields
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_master(H, c, A, l, u, xmin, xmax, x0, opt)
x = qps_master(H, c, A, l, u)
x = qps_master(H, c, A, l, u, xmin, xmax)
x = qps_master(H, c, A, l, u, xmin, xmax, x0)
x = qps_master(H, c, A, l, u, xmin, xmax, x0, opt)
x = qps_master(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_master(...)
[x, f] = qps_master(...)
[x, f, exitflag] = qps_master(...)
[x, f, exitflag, output] = qps_master(...)
[x, f, exitflag, output, lambda] = qps_master(...)
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_master(H, c, A, l, u, xmin, [], x0, opt);