| lpcdd {rcdd} | R Documentation |
Solve linear program or explain why it has no solution.
lpcdd(hrep, objgrd, objcon = as(0, class(objgrd)), minimize = TRUE,
solver = c("DualSimplex", "CrissCross"))
hrep |
H-representation of convex polyhedron (see details) over which an affine function is maximized or minimized. |
objgrd |
gradient vector of affine function. |
objcon |
constant term of affine function. |
minimize |
minimize if TRUE, otherwise maximize. |
solver |
type of solver. Use the default unless you know better. |
See cddlibman.pdf in the doc directory of this package,
especially Sections 1 and 2 and the documentation of the function
dd_LPSolve in Section 4.2.
This function minimizes or maximizes an affine function x
maps to sum(objgrd * x) + objcon over a convex polyhedron
given by the H-representation given by the matrix hrep.
Let
l <- hrep[ , 1]
b <- hrep[ , 2]
v <- hrep[ , - c(1, 2)]
a <- (- v)
Then the convex polyhedron in question is the set of
points x satisfying
axb <- a %*% x - b
all(axb <= 0)
all(l * axb == 0)
a list containing some of the following components:
solution.type |
character string describing the solution type.
"Optimal" indicates the optimum is achieved.
"Inconsistent" indicates the feasible region is empty
(no points satisfy the constraints, the polyhedron specified
by hrep is empty).
"DualInconsistent" or "StrucDualInconsistent" indicates
the feasible region is unbounded
and the objective function is unbounded below when minimize = TRUE
or above when minimize = FALSE. |
primal.solution |
Returned only when solution.type = "Optimal",
the solution to the stated (primal) problem. |
dual.solution |
Returned only when solution.type = "Optimal",
the solution to the dual problem, Lagrange multipliers for the primal
problem. |
dual.direction |
Returned only when
solution.type = "Inconsistent",
coefficients of the positive combination of original inequalities
that proves the inconsistency. |
primal.direction |
Returned only when
solution.type = "DualInconsistent"
or solution.type = "StrucDualInconsistent",
coefficients of the linear combination of columns
that proves the dual inconsistency, also an unbounded direction
for the primal LP. |
The arguments hrep, objgrd, and objcon may
have type "character" in which case their elements are interpreted
as unlimited precision rational numbers. They consist of an optional
minus sign, a string of digits of any length (the numerator),
a slash, and another string of digits of any length (the denominator).
The denominator must be positive. If the denominator is one, the
slash and the denominator may be omitted. The cdd package
provides several functions (see ConvertGMP and ArithmeticGMP)
for conversion back and forth between R floating point numbers and rationals
and for arithmetic on GMP rationals.
scdd, ArithmeticGMP,
ConvertGMP
# first two rows are inequalities, second two equalities
hrep <- rbind(c("0", "0", "1", "1", "0", "0"),
c("0", "0", "0", "2", "0", "0"),
c("1", "3", "0", "-1", "0", "0"),
c("1", "9/2", "0", "0", "-1", "-1"))
a <- c("2", "3/5", "0", "0")
lpcdd(hrep, a)
# primal inconsistent problem
hrep <- rbind(c("0", "0", "1", "0"),
c("0", "0", "0", "1"),
c("0", "-2", "-1", "-1"))
a <- c("1", "1")
lpcdd(hrep, a)
# dual inconsistent problem
hrep <- rbind(c("0", "0", "1", "0"),
c("0", "0", "0", "1"))
a <- c("1", "1")
lpcdd(hrep, a, minimize = FALSE)