linear programming solver
[x,lagr,f]=linpro(p,C,b [,x0]) [x,lagr,f]=linpro(p,C,b,ci,cs [,x0]) [x,lagr,f]=linpro(p,C,b,ci,cs,me [,x0]) [x,lagr,f]=linpro(p,C,b,ci,cs,me,x0 [,imp])
real column vector (dimension n
)
real matrix (dimension m x n
) (If no
constraints are given, you can set C = []
)
RHS column vector (dimension m
) (If no
constraints are given, you can set b = []
)
column vector of lower-bounds (dimension n
). If there are no lower bound constraints, put
ci = []
. If some components of x
are bounded from below, set the other (unconstrained) values
of ci
to a very large negative number
(e.g. ci(j) = -number_properties('huge')
.
column vector of upper-bounds. (Same remarks as above).
number of equality constraints (i.e. C(1:me,:)*x
= b(1:me)
)
either an initial guess for x
or one of
the character strings 'v'
or
'g'
. If x0='v'
the calculated
initial feasible point is a vertex. If x0='g'
the calculated initial feasible point is arbitrary.
verbose option (optional parameter) (Try
imp=7,8,...
) warning the message are output in
the window where scilab has been started.
optimal solution found.
optimal value of the cost function (i.e. f=p'*x
).
vector of Lagrange multipliers. If lower and
upper-bounds ci,cs
are provided,
lagr
has n + m
components and
lagr(1:n)
is the Lagrange vector associated
with the bound constraints and lagr (n+1 : n +
m)
is the Lagrange vector associated with the linear
constraints. (If an upper-bound (resp. lower-bound)
constraint i
is active lagr(i)
is
> 0 (resp. <0). If no bounds are provided,
lagr
has only m
components.
[x,lagr,f]=linpro(p,C,b [,x0])
Minimize
p'*x
under the constraints C*x <=
b
[x,lagr,f]=linpro(p,C,b,ci,cs [,x0])
Minimize
p'*x
under the constraints C*x <= b
,
ci <= x <= cs
[x,lagr,f]=linpro(p,C,b,ci,cs,me [,x0])
Minimize p'*x
under the constraints
If no initial point is given the
program computes a feasible initial point
which is a vertex of the region of feasible points if
x0='v'
.
If x0='g'
, the program computes a feasible initial
point which is not necessarily a vertex. This mode is
advisable when the quadratic form is positive
definite and there are a few constraints in
the problem or when there are large bounds
on the variables that are security bounds and
very likely not active at the optimal solution.
, Universidad de Cantabria,
, Universidad de Cantabria
E. Casas and C. Pola, An algorithm for indefinite quadratic programming based on a partial Cholesky factorization, RAIRO-Recherche Opérationnelle/Operations Research, 27 (1993), 401-426.
in routines/optim directory (authors E.Casas, C. Pola Mendez):
anfm01.f anfm03.f anfm05.f anrs01.f auxo01.f dimp03.f dnrm0.f optr03.f pasr03.f zthz.f anfm02.f anfm04.f anfm06.f anrs02.f desr03.f dipvtf.f optr01.f opvf03.f plcbas.f
From BLAS library
daxpy.f dcopy.f ddot.f dnrm2.f dscal.f dswap.f idamax.f
in routines/calelm directory (authors INRIA):
add.f ddif.f dmmul.f
From LAPACK library : dlamch.f