H101: Linear Optimization Using the Simplex Algorithm

Author(s): M. Gyr	Library: MATHLIB
Submitter: K.S. Kölbig	Submitted: 15.02.1994
Language: Fortran	Revised:

Subroutine subprograms RSMPLX and DSMPLX calculate the quantities for which the linear form, or objective function,

assumes a maximum value subject to the inequality constraints

and the equality constraints

A number of the variables can be restricted to non-negative values ( ). The remaining variables are then unrestricted ( ). In the case , all variables are unrestricted. These subprograms can also be used for the so-called degenerate case.

On computers other than CDC or Cray, only the double-precision version DSMPLX is available. On CDC and Cray computers, only the single precision version RSMPLX is available.

Structure:

SUBROUTINE subprograms
User Entry Names: RSMPLX, DSMPLX
Internal Entry Names: H101S1, H101S2
Files Referenced: Unit 6
External References: MTLMTR, ABEND

Usage:

For (type REAL), (type DOUBLE PRECISION),

    CALL tSMPLX(A,B,C,Z0,IDA,M,M1,N,N1,LW,IDW,W,X,Z,ITYPE)

A

(type according to t) Two-dimensional array of dimension . Contains, on entry, the coefficients . Destroyed during execution.

B

(type according to t) One-dimensional array of dimension . Contains, on entry, the coefficients . Destroyed during execution.

C

(type according to t) One-dimensional array of dimension . Contains, on entry, the coefficients . Destroyed during execution.

Z0

(type according to t) Contains, on entry, the initial value of the objective function.

IDA

(INTEGER) Declared first dimension of A in the calling program ( ).

M

(INTEGER) The total number m of variables ( ).

M1

(INTEGER) The number of restricted variables ( .

N

(INTEGER) The total number n of constraints ( ).

N1

(INTEGER) The number of inequality constraints ( .

LW

(INTEGER) Two-dimensional array of dimension . Used as working space.

IDW

(INTEGER) Declared first dimension of LW in the calling program ( ).

W

(type according to t) One-dimensional array of dimension . Used as working space.

X

(type according to t) One-dimensional array of dimension . If or , its first m elements X(1),...,X(M) contain, on exit, the or a solution , respectively. The next n elements X(M+1),...,X(M+N) contain the values of the so-called slack variables . If or , the elements are undefined.

Z

(type according to t) If or , Z contains, on exit, the result z of the objective function. Undefined for and .

ITYPE

(INTEGER) Defines, on exit, the type of the result:

There is exactly one finite solution.

There is more than one solution.

There is no finite solution.

There is no feasable initial solution.

Method:

The method is described in Ref. 1 and Ref. 2.

Error handling:

Error H101.1: or .
Error H101.2: or or or .
In both cases, a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

References:

1. H.P. Künzi, H.G. Tzschach and C.A. Zehnder, Numerical methods of mathematical optimization, (Academic Press, New York 1968)
2. E. Stiefel, Einführung in die Numerische Mathematik, (B.G. Teubner, Stuttgart 1965)