Adding Rows to a Problem: Example lpex3.c

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This example illustrates how to develop your own solution algorithms with routines from the Callable Library. It also shows you how to add rows to a problem object. Here is the problem that lpex3 solves:

Minimize	c^Tx
subject to	Hx = d   Ax = b   l x u
where	H =	( -1 0 1 0 1 0 0 0 )	d =	( -3 )
		( 1 -1 0 1 0 0 0 0 )		( 1 )
		( 0 1 -1 0 0 1 -1 0 )		( 4 )
		( 0 0 0 -1 0 -1 0 1 )		( 3 )
		( 0 0 0 0 -1 0 1 -1 )		( -5 )
	A =	( 2 1 -2 -1 2 -1 -2 -3 )	b =	( 4 )
		( 1 -3 2 3 -1 2 1 1 )		( -2 )
	c =	(-9 1 4 2 -8 2 8 12 )
	l =	( 0 0 0 0 0 0 0 0 )
	u =	(50 50 50 50 50 50 50 50 )

0. The ILOG CPLEX Network Optimizer is used to solve

   Minimize	c^Tx
   subject to	Hx = d  l x u

1. The constraints Ax=b are added to the problem, and the dual simplex optimizer is used to solve the new problem, starting at the optimal basis of the simpler network problem.

The example first calls CPXopenCPLEX to create the environment and then turns on the ILOG CPLEX screen indicator (CPX_PARAM_SCRIND). Next it sets the simplex display level (CPX_PARAM_SIMDISPLAY) to 2 to indicate iteration-by-iteration output, so that the progress of each iteration of the optimizer can be observed. Setting this parameter to 2 is not generally recommended; the example does so only for illustrative purposes.

The example creates a problem object by a call to CPXcreateprob. Then the network data is copied via a call to CPXcopylp. After the network data is copied, the parameter CPX_PARAM_LPMETHOD is set to CPX_ALG_NET and the routine CPXlpopt is called to solve the network part of the optimization problem using the network optimizer. The objective value of this problem is retrieved by CPXgetobjval.

Then the extra rows are added by CPXaddrows. For convenience, the total number of nonzeros in the rows being added is stored in an extra element of the array rmatbeg, and this element is passed for the parameter nzcnt. The name arguments to CPXaddrows are NULL, since no variable or constraint names were defined for this problem.

After the CPXaddrows call, the parameter CPX_PARAM_LPMETHOD is set to CPX_ALG_DUAL and the routine CPXlpopt is called to re-optimize the problem using the dual simplex optimizer. After re-optimization, CPXsolution accesses the solution status, the objective value, and the primal solution. NULL is passed for the other solution values, since the information they provide is not needed in this example.

At the end, the problem is written as a SAV file by CPXwriteprob. This file can then be read into the ILOG CPLEX Interactive Optimizer to analyze whether the problem was correctly generated. Using a SAV file is recommended over MPS and LP files, as SAV files preserve the full numeric precision of the problem.

After the TERMINATE: label, CPXfreeprob releases the problem object, and CPXcloseCPLEX releases the ILOG CPLEX environment.