Geometric programming
The solver MOSEK is capable of solving a sub-class of geometric problems where c≥0 with the additional constraint t≥0, so called posynomial geometric programming. The following example is taken from the MOSEK manual. (note, the positivity constraint on t will be added automatically)
If the geometric program violates the posynomial assumption, an error will be issued.
YALMIP will automatically convert some simple violations of the posynomial assumptions, such as lower bounds on monomial terms and maximization of negative monomials. The following small program maximizes the volume of an open box, under constraints on the floor and wall area, and constraints on the relation between the height, width and depth (example from [S. Boyd, S. Kim, L. Vandenberghe, A. Hassibi] ).
Generalized geometric programmingSome geometric programs, although not given in standard form, can still be solved using a standard geometric programming solver after some some additional variables and constraints have been introduced. YALMIP has built-in support for some of these conversion. To begin with, nonlinear operators can be used also in geometric programs, as in any other optimization problems (as long as YALMIP is capable of proving convexity, see the nonlinear operator examples)
Powers of posynomials are allowed in generalized geometric programs. YALMIP will automatically take care of this and convert the problems to a standard geometric programs. Note that the power has to be positive if used on the left-hand side of a <, and negative otherwise.
To understand how a generalized geometric program can be converted to a standard geometric program. the reader is referred to [S. Boyd, S. Kim, L. Vandenberghe, A. Hassibi] |