Global Optimisation #9

eeshan9815 · 2018-06-19T16:33:24Z

No description provided.

codecov-io · 2018-06-20T11:59:52Z

Codecov Report

Merging #9 into master will decrease coverage by 56.29%.
The diff coverage is 0%.

@@            Coverage Diff             @@
##           master       #9      +/-   ##
==========================================
- Coverage   81.08%   24.78%   -56.3%     
==========================================
  Files           3        3              
  Lines          37      117      +80     
==========================================
- Hits           30       29       -1     
- Misses          7       88      +81

Impacted Files	Coverage Δ
src/SortedVectors.jl	`71.42% <ø> (ø)`	⬆️
src/optimise1.jl	`0% <0%> (ø)`

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dpsanders · 2018-06-20T15:48:18Z

src/optimise1.jl

+
+import Base.isless
+
+struct IntervalMinima{T<:Real}


"Minimum" is the singular; "minima" is the plural.

You want "minimum" everywhere.

Okay. Using global_minimum instead since minimum is an existent binding.

dpsanders · 2018-06-20T15:49:19Z

src/optimise1.jl

+    Q = binary_minheap(IntervalMinima{T})
+
+    minima = f(interval(mid(x))).hi
+    arg_minima = Interval{T}[]


"Minima" is correct here since there may be several.

dpsanders

LGTM, thanks.

dpsanders · 2018-07-23T20:14:28Z

examples/optimise1.jl

+
+
+# Unconstrained Optimisation
+f(x, y) = (1.5 - x * (1 - y))^2 + (2.25 - x * (1 - y^2))^2 + (2.625 - x * (1 - y^3))^2


Please include the source for test cases and solutions.

dpsanders · 2018-07-23T20:18:29Z

There are some test cases here:

https://github.com/JuliaNLSolvers/OptimTestProblems.jl

dpsanders · 2018-07-23T20:19:09Z

See also the links at
https://github.com/JuliaIntervals/IntervalRootFinding.jl/blob/master/examples/roots.jl

dpsanders · 2018-07-24T03:07:34Z

src/optimise1.jl

+    return lb..global_minimum, arg_minima
+end
+
+function minimise1d_deriv(f::Function, x::Interval{T}; reltol=1e-3, abstol=1e-3) where {T<:Real}


There seems to be a lot of common code between this function and minimise1d. Can that be refactored out, or can these functions be combined?

I'll add deriv as a kwarg and combine the functions

dpsanders · 2018-07-24T03:07:52Z

src/optimise1.jl

+    return lb..global_minimum, arg_minima
+end
+
+function minimise_icp_constrained(f::Function, x::IntervalBox{N, T}, constraints::Vector{constraint{T}} = Vector{constraint{T}}(); reltol=1e-3, abstol=1e-3) where {N, T<:Real}


There seems to be a lot of common code between this function and the previous one. Can that be refactored out, or can these functions be combined?

I added them differently because the GODOWN used for them is different, as we can use the mid in the unconstrained case and that causes better convergence, whereas it's not possible in the constrained case since mid might not be satisfied by the constraints.
Also, the robust constrained optimisation function will be different and will include John conditions, so I kept them separate for now.
Should I combine them using runtime checks?

dpsanders · 2018-07-24T03:08:26Z

src/optimise1.jl

+        # if 0 .∉ ForwardDiff.gradient(f, p.intval.v)
+        #     continue
+        # end
+        X = icp(f, p.intval, -∞..global_minimum)


dpsanders · 2018-07-24T03:08:55Z

src/optimise1.jl

+import Base.isless
+
+struct IntervalMinima{T<:Real}
+    intval::Interval{T}


I would prefer to write out interval

dpsanders · 2018-07-24T03:16:13Z

Please add more test cases.

dpsanders · 2018-07-24T03:09:09Z

src/optimise1.jl

+
+import Base.isless
+
+struct IntervalMinima{T<:Real}


This is a single minimum.

Right, sorry about this.

dpsanders · 2018-07-24T03:09:31Z

src/optimise1.jl

+
+struct IntervalMinima{T<:Real}
+    intval::Interval{T}
+    global_minimum::T


You can use minimum here.

dpsanders · 2018-07-24T03:09:47Z

src/optimise1.jl

+    global_minimum::T
+end
+
+function isless(a::IntervalMinima{T}, b::IntervalMinima{T}) where {T<:Real}


You can write this as a single-line function.

dpsanders · 2018-07-24T03:12:04Z

src/optimise1.jl

+            continue
+        end
+
+        deriv = ForwardDiff.derivative(f, p.intval)


It should be optional to use this.

dpsanders · 2018-07-24T03:12:44Z

src/optimise1.jl

+            continue
+        end
+        # Second derivative contractor
+        # doublederiv = ForwardDiff.derivative(x->ForwardDiff.derivative(f, x), p.intval)


It should be optional to use this. Is there a way of setting up the 2nd derivative beforehand to reduce the workload?

Okay.
I removed it because the second deriv evaluation is costly, and since the interval to be computed over is different for each iteration, it can slow down the function.
Also, it didn't show any improvements over the first deriv contractor

dpsanders · 2018-07-24T03:14:12Z

src/optimise1.jl

+
+
+
+struct IntervalBoxMinima{N, T<:Real}


dpsanders · 2018-07-24T03:14:32Z

src/optimise1.jl

+
+
+struct IntervalBoxMinima{N, T<:Real}
+    intval::IntervalBox{N, T}


You don't need a separate type here -- just reuse IntervalMinimum.

dpsanders · 2018-07-24T03:15:00Z

src/optimise1.jl

+end
+
+struct constraint{T<:Real}
+    f::Function


This should be a type parameter of the Constraint type for efficiency.

dpsanders · 2018-07-24T03:15:11Z

src/optimise1.jl

+    global_minimum::T
+end
+
+struct constraint{T<:Real}


Initial capital for types.

dpsanders · 2018-07-24T03:15:24Z

src/optimise1.jl

+    global_minimum::T
+end
+
+struct constraint{T<:Real}


dpsanders · 2018-07-25T20:15:19Z

I think that IntervalConstraintProgramming.jl needs to be added to REQUIRE?

dpsanders · 2018-08-21T01:26:53Z

src/optimise1.jl

+
+Base.isless(a::IntervalBoxMinimum{N, T}, b::IntervalBoxMinimum{N, T}) where {N, T<:Real} = isless(a.minimum, b.minimum)
+
+function minimise_icp(f::Function, x::IntervalBox{N, T}; reltol=1e-3, abstol=1e-3) where {N, T<:Real}


Make this a method of minimise and dispatch on a type ICP or similar.

dpsanders · 2018-08-21T01:27:08Z

src/optimise1.jl

+    return lb..global_minimum, arg_minima
+end
+
+function minimise_icp_constrained(f::Function, x::IntervalBox{N, T}, constraints::Vector{Constraint{T}} = Vector{Constraint{T}}(); reltol=1e-3, abstol=1e-3) where {N, T<:Real}


Make this a method of minimise and dispatch on a type.

Fix deprecated syntax for inner constructor of SortedVector

2499f85

eeshan9815 force-pushed the global_min branch from c7910e0 to c161245 Compare June 20, 2018 11:59

Initial implementation of global optimisation

4099735

eeshan9815 force-pushed the global_min branch from c161245 to 4099735 Compare June 20, 2018 14:52

dpsanders reviewed Jun 20, 2018

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eeshan9815 added 2 commits July 19, 2018 19:31

Add derivative contractors

a9c1eab

Add icp contractors

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dpsanders reviewed Jul 23, 2018

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dpsanders requested changes Jul 24, 2018

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eeshan9815 added 2 commits August 2, 2018 06:12

Incorporate changes from review comments

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Remove parameterization of F

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Global Optimisation #9

Global Optimisation #9

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		# Unconstrained Optimisation
		f(x, y) = (1.5 - x * (1 - y))^2 + (2.25 - x * (1 - y^2))^2 + (2.625 - x * (1 - y^3))^2



		struct IntervalBoxMinima{N, T<:Real}
		intval::IntervalBox{N, T}


		Base.isless(a::IntervalBoxMinimum{N, T}, b::IntervalBoxMinimum{N, T}) where {N, T<:Real} = isless(a.minimum, b.minimum)

		function minimise_icp(f::Function, x::IntervalBox{N, T}; reltol=1e-3, abstol=1e-3) where {N, T<:Real}

Global Optimisation #9

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