| Constraint matrix, A |
|
Constraint matrix in COO(a)
format. • |
Solves a Linear Programming
(LP) problem using the CPLEX API from a Fortran 90 program,
The problem matrix data are introduced
in sparse-matrix coordinates (COO(a)) mode,
instead of full matrix (as practical LP problems are typically sparse),
so, only the nonzero values are given. For the matrix data,
the CPLEX API accepts only sparse formats,
here the "compressed sparse column" (CSC) necessary for
the 'CPXcopylp' routine, which expects the other data
(vectors) in full. The program internally converts COO
into "compressed sparse column", CSC [Wikipedia].
In COO, for each nonzero value,
a(i,j), i = 1..nconstr,
j = 1..nvar, only the 3 values
of i, j, and a(i,j) are given.
(Commas are optional, just for readability.)
Draws graphs for: the final, optimum values
of the variables, xi;
their contributions to the objective function,
ci xi;
and the iteration steps till optimum (CPLEX internal algorithm).
This webpage uses 'base64' images, as also does the Runge-Kutta
prototype.
The base problem ("diet", from SAS [SAS/OR])
gives zMIN = 12.08. Data for another problem ("jam",
from Ramalhete et al. [1985]), are also supplied,
giving zMAX = 1021.3.
To be presented at CISTI'2019,
Conferência Ibérica de Sistemas e Tecnologias de Informação
(Iberian Conference on Systems and Information Technologies),
June 2019, Coimbra (Portugal).
(a)
COO, matrix coordinates [Wikipedia; Python].
|
■ CPLEX
• IBM ILOG CPLEX Optimizer
• Wikipedia: CPLEX
• Google CPXcopylp
■ Sparse matrix
• Wikipedia: Sparse matrix
• (Python) scipy.sparse.coo_matrix,
sparse matrix in COOrdinate format or ‘ijv’ or ‘triplet’ format.
• SAS/OR Example 6.1
Diet Problem.
• UTF-8 Geometric Shapes.
• Ramalhete, M.,
J. Guerreiro, A. Magalhães,
1985, «Programação Linear» (Linear Programming), Vol. I,
McGraw-Hill, 2 «Aplicações da Programação Linear» (Applications
of LP), 2.16, Probl. 14, p 93.
• 1687-10-14: Simson, Robert
(† 1768-10-01). |
