Add solvers to README (#98)

* Add solvers to README

* Add SAGE

* Fix

* Update

Author: blegat

README.md

@@ -5,8 +5,11 @@
 
 [PolyJuMP.jl](https://github.com/jump-dev/PolyJuMP.jl) is a [JuMP](https://github.com/jump-dev/JuMP.jl)
 extension for formulating and solving polynomial optimization problems.
+This extension includes the following:
 
-These problems can then be solved using [SumOfSquares.jl](https://github.com/jump-dev/SumOfSquares.jl).
+* Polynomial functions on JuMP decisions variables. These can be solved with the `PolyJuMP.QCQP.Optimizer` or `PolyJuMP.KKT.Optimizer`.
+* Constraints that a polynomial is nonnegative where the coefficients of the polynomials depend on JuMP decision variables.
+  These nonnegativity constraints can be reformulated using sufficient conditions using `PolyJuMP.RelativeEntropy` submodule or [SumOfSquares.jl](https://github.com/jump-dev/SumOfSquares.jl).
 
 ## License
 
@@ -20,6 +23,53 @@ import Pkg
 Pkg.add("PolyJuMP")
 ```
 
+## Use with JuMP
+
+To use QCQP solver with JuMP, use a nonconvex QCQP solver, e.g., `Gurobi.Optimizer` and `PolyJuMP.QCQP.Optimizer`:
+
+```julia
+using JuMP, PolyJuMP, Gurobi
+model = Model(() -> PolyJuMP.QCQP.Optimizer(Gurobi.Optimizer))
+```
+
+To use KKT solver with JuMP, use solver of algebraic systems of equations implementing the [SemialgebraicSets interface](https://github.com/JuliaAlgebra/SemialgebraicSets.jl), e.g., `HomotopyContinuation.SemialgebraicSetsHCSolver` and `PolyJuMP.KKT.Optimizer`:
+
+```julia
+using JuMP, PolyJuMP, HomotopyContinuation
+model = Model(optimizer_with_attributes(
+    PolyJuMP.KKT.Optimizer,
+    "solver" => HomotopyContinuation.SemialgebraicSetsHCSolver(),
+))
+```
+
+For a nonnegativity constraint on a polynomial, e.g.,
+```julia
+using DynamicPolynomials
+@polyvar x y
+using JuMP
+model = Model()
+@variable(model, a)
+@constraint(model, a * x * y^2 + y^3 >= a * x)
+```
+you need to specify how to interpret this nonnegativity constraint. To use Sum-of-Arithmetic-Geometric-Exponentials (SAGE), use
+```julia
+import PolyJuMP
+PolyJuMP.setpolymodule!(model, PolyJuMP.SAGE)
+```
+To use Sum-of-Squares (SOS), use
+```julia
+import SumOfSquares
+PolyJuMP.setpolymodule!(model, SumOfSquares)
+```
+or replace `model = Model()` by `model = SOSModel()`.
+
+Alternatively, the nonnegativity constraint can be explicit:
+```julia
+@constraint(model, a * x * y^2 + y^3 - a * x in PolyJuMP.SAGE.Polynomials())
+@constraint(model, a * x * y^2 + y^3 - a * x in SumOfSquares.SOSCone())
+```
+This allows mixing SAGE and SOS constraints in the same model.
+
 ## Documentation
 
 Documentation for `PolyJuMP.jl` is included in the