add example with powermean cone

docs/src/examples.md

@@ -14,6 +14,7 @@ New examples are welcomed and should be implemented similarly to the existing ex
 - [Convexity parameter.](https://github.com/chriscoey/Hypatia.jl/tree/master/examples/convexityparameter) Find the strong convexity parameter of a polynomial function over a domain.
 - [Covariance estimation.](https://github.com/chriscoey/Hypatia.jl/tree/master/examples/covarianceest) Estimate a covariance matrix that satisfies some given prior information and minimizes a given convex spectral function.
 - [Density estimation.](https://github.com/chriscoey/Hypatia.jl/tree/master/examples/densityest) Find a valid polynomial density function maximizing the log likelihood of a set of observations.
+- [Discrete maximum likelihodd.](https://github.com/chriscoey/Hypatia.jl/tree/master/examples/discretemaxlikelihood) Maximize likelihood of observations at discrete points, subject to probability vector not being too far from a uniform prior.
 - [D-optimal design.](https://github.com/chriscoey/Hypatia.jl/tree/master/examples/doptimaldesign) Solve a D-optimal experiment design problem, i.e. maximize the determinant of the information matrix subject to side constraints.
 - [Entanglement-assisted capacity.](https://github.com/chriscoey/Hypatia.jl/tree/master/examples/entanglementassisted) Compute the entanglement-assisted classical capacity of a quantum channel.
 - [Experiment design.](https://github.com/chriscoey/Hypatia.jl/tree/master/examples/experimentdesign) Solve a general experiment design problem that minimizes a given convex spectral function of the information matrix subject to side constraints.

examples/Examples.jl

@@ -38,6 +38,7 @@ const JuMP_examples = [
     "convexityparameter",
     "covarianceest",
     "densityest",
+    "discretemaxlikelihood",
     "doptimaldesign",
     "entanglementassisted",
     "experimentdesign",

examples/discretemaxlikelihood/JuMP.jl

@@ -0,0 +1,30 @@
+#=
+maximize likelihood of d observations at discrete points appearing with random
+frequencies, subject to probability vector not being too far from a uniform
+prior
+=#
+
+struct DiscreteMaxLikelihood{T <: Real} <: ExampleInstanceJuMP{T}
+    d::Int
+end
+
+function build(inst::DiscreteMaxLikelihood{T}) where {T <: Float64}
+    d = inst.d
+    @assert d >= 2
+    freq = rand(1:(2 * d), d)
+
+    model = JuMP.Model()
+    JuMP.@variables(model, begin
+        p[1:d] >= 0
+        prodp
+    end)
+    JuMP.@constraints(model, begin
+        vcat(prodp, p) in Hypatia.HypoPowerMeanCone{T}(freq / sum(freq))
+        vcat(inv(d), inv(d), p) in Hypatia.EpiPerSepSpectralCone{T}(
+            Cones.NegEntropySSF(), Cones.VectorCSqr{T}, d)
+        sum(p) == 1
+    end)
+    JuMP.@objective(model, Max, prodp)
+
+    return model
+end

examples/discretemaxlikelihood/JuMP_test.jl

@@ -0,0 +1,16 @@
+
+insts = Dict()
+insts["minimal"] = [
+    ((2,),),
+    ]
+insts["fast"] = [
+    ((10,),),
+    ((100,),),
+    ((1000,),),
+    ]
+insts["various"] = [
+    ((2500,),),
+    ((5000,),),
+    ((10000,),),
+    ]
+return (DiscreteMaxLikelihood, insts)