Geometric programming preview

Geometric programs (GP) can be conveniently expressed in conic form using the exponential cone
$$ x\geq y\exp(z/y),\quad y>0$$
in the upcoming version 9 of MOSEK. Here is a preview implementation of some signal-to-interference-and-noise optimization problems in Python Fusion:

http://nbviewer.jupyter.org/github/MOSEK/Tutorials/blob/version9/sinr-optimization/sinr-optimization.ipynb

The key log-sum-exp constraint is just a few lines:

	# Models log(sum(exp(Ax+b))) <= 0.
	# Each row of [A b] describes one of the exp-terms
	def logsumexp(M, A, x, b):
	u = M.variable(A.shape[0])
	M.constraint( Expr.sum(u), Domain.lessThan(1.0))
	M.constraint( Expr.hstack(u,
	Expr.constTerm(A.shape[0], 1.0),
	Expr.add(Expr.mul(A, x), b)), Domain.inPExpCone())

view raw logsumexp.py hosted with ❤ by GitHub

You can read more about modeling GPs in our Modeling Cookbook:

https://docs.mosek.com/modeling-cookbook/expo.html#geometric-programming

MOSEK's previous GP interface (scopt/dgopt/expopt), which is being phased out, relied on the slower and less accurate general nonlinear optimizer. You can read more about version 9 plans in

https://themosekblog.blogspot.com/2018/01/version-9-roadmap_31.html