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amplide
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- Abacus College, Oxford
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Using AMPL/MINOS
MINOS is an optimization package for linear and nonlinear mathematical programs in continu-
ous variables. This supplement to AMPL: A Modeling Language for Mathematical Programming
describes the most important features of MINOS for AMPL users. Further information on MINOS is
available from:
Stanford Business Software, Inc.
2672 Bayshore Parkway, Suite 304
Mountain View, CA 94043
415-962-8719; fax 415-962-1869
Section §1 below describes the kinds of problems to which MINOS is applicable, and Section
§2 explains in general terms how solver-specific directives can be passed from AMPL to MINOS.
Sections §3 and §4 then briefly introduce the algorithms that MINOS uses for linear and for nonlin-
ear programming, respectively, and describe the relevant algorithmic directives. Section §5 pre-
sents directives for controlling listings from MINOS, and Section §6 discusses options for restarting
from a known solution or basis.
§1 Applicability
MINOS is designed to solve the linear programs described in Chapters 1-8 and 11-12 of AMPL:
A Modeling Language for Mathematical Programming, as well as the ‘‘smooth’’ nonlinear pro-
grams described in Chapter 13. Smooth nonlinear functions can be accommodated in both the
objective and the constraints; nonlinear equation systems may also be solved by omitting an objec-
tive. Nonsmooth nonlinearities are also accepted, but MINOS is not designed for them and in gen-
eral will not produce reliable results when they are present.
MINOS does not solve integer programs as described in Chapter 15. When presented with an
integer program, MINOS ignores the integrality restrictions on the variables, as indicated by a mes-
sage such as
MINOS 5.4: ignoring integrality of 5 variables
It then solves the continuous relaxation of the resulting problem, and returns a solution in which
some of the integer variables may have fractional values.
MINOS can solve piecewise-linear programs, as described in Chapter 14, provided that they sat-
isfy certain rules that permit them to be transformed to linear programs. Any piecewise-linear term
in a minimized objective must be convex, its slopes forming an increasing sequence as in:
<<-1,1,3,5; -5,-1,0,1.5,3>> x[j]
Any piecewise-linear term in a maximized objective must be concave, its slopes forming a decreas-
ing sequence as in:
<<1,3; 1.5,0.5,0.25>> x[j]
, 2 USING AMPL/MINOS
In the constraints, any piecewise-linear term must be either convex and on the left-hand side of a ≤
constraint (or equivalently, the right-hand side of a ≥ constraint), or else concave and on the left-
hand side of a ≥ constraint (or equivalently, the right-hand side of a ≤ constraint). AMPL automati-
cally converts the piecewise-linear program to a linear one, sends the latter to MINOS, and converts
the solution back; the conversion has the effect of adding a variable to correspond to each linear
piece. Piecewise-linear programs that violate the above rules are converted to integer programs,
which are treated as described in the preceding paragraph; MINOS returns a solution to the continu-
ous relaxation of the equivalent integer program, which in general is not optimal for the original
piecewise-linear problem.
§2 Controlling MINOS from AMPL
In many instances, you can successfully apply MINOS by simply specifying a model and data,
setting the solver option to minos, and typing solve. For larger linear programs and more
difficult nonlinear programs, however, you may need to pass specific directives to MINOS to obtain
the desired results.
To give directives to MINOS, you must first assign an appropriate character string to the AMPL
option called minos_options. When solve invokes MINOS, it breaks this string into a series
of individual directives. Here is an example:
ampl: model diet.mod;
ampl: data diet.dat;
ampl: option solver minos;
ampl: option minos_options ’crash_option=0 \
ampl? feasibility_tolerance=1.0e-8 scale=no \
ampl? iterations_limit=100’;
ampl: solve;
MINOS 5.4:
crash_option=0
feasibility_tolerance=1.0e-8
scale=no
iterations_limit=100
MINOS 5.4: optimal solution found.
4 iterations, objective 88.2
MINOS confirms each directive; it will display an error message if it encounters one that it does not
recognize.
All of the directives described below have the form of an identifier, an = sign, and a value;
unlike AMPL, MINOS treats upper-case and lower-case letters as being the same. You may store
any number of concatenated directives in minos_options. The example above shows how to
type all the directives in one long string, using the \ character to indicate that the string continues
on the next line. Alternatively, you can list several strings, which AMPL will automatically con-
catenate:
ampl: option minos_options ’crash_option=0’
ampl? ’ feasibility_tolerance=1.0e-8 scale=no’
ampl? ’ iterations_limit=100’;
In this form, you must take care to supply the space that goes between the directives; here we have
put it before feasibility_tolerance and iterations_limit.
If you have specified the directives above, and then want to set optimality_tolerance
to 1.0e–8 and change crash_option to 1, you might think to type:
ampl: option minos_options
ampl? ’optimality_tolerance=1.0e-8 crash_option=1’;
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