algstat (version 0.0.2)

polyOptim: Polynomial Optimization

Description

Find the collection of critical points of a multivariate polynomial unconstrained or constrained to an affine variety (algebraic set; solution set of multivariate polynomials).

Usage

polyOptim(objective, constraints, varOrder, ...)

Arguments

objective

the objective polynomial (as a character or mpoly)

constraints

(as a character or mpoly/mpolyList)

varOrder

variable order (see examples)

...

stuff to pass to bertini

Value

an object of class bertini

Examples

## Not run: 
# 
# # unconstrained optimization of polynomial functions is available
# polyOptim("x^2")
# polyOptim("-x^2")
# polyOptim("-(x - 2)^2")
# polyOptim("-(x^2 + y^2)")
# polyOptim("-(x^2 + (y - 2)^2)")
# 
# polyOptim("(x - 1) (x - 2) (x - 3)") # fix global labeling
# 
# 
# # constrained optimization over the affine varieties is also available
# # (affine variety = solution set of polynomial equations)
# 
# # find the critical points of the plane f(x,y) = x + y
# # over the unit circle x^2 + y^2 = 1
# polyOptim("x + y", "x^2 + y^2 = 1")
# 
# # you can specify them as a combo of mpoly, mpolyList, and characters
# o <- mp("x + y")
# c <- "x^2 + y^2 = 1"
# polyOptim(o, c)
# 
# c <- mp("x^2 + y^2 - 1")
# polyOptim(o, c)
# 
# out <- polyOptim("x + y", c)
# str(out)
# 
# # another example, note the solutions are computed over the complex numbers
# polyOptim("x^2 y", "x^2 + y^2 = 3")
# # solutions: (+-sqrt(2), +-1) and (0, +-sqrt(3))
# 
# 
# 
# 
# ## End(Not run)