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Problem 9,10 and 16 (#396)
* Problem 9 and 10 * feat(trigb): add banded trigonometric problem (Meta, ADNLP, PureJuMP) * trigb.jl * Update trig.jl * Apply suggestions from code review Co-authored-by: Tangi Migot <tangi.migot@gmail.com> * removing unnecessary variables * fixing remaining mentions of xi variable * removing twice renditions * meta * PureJuMP * Update toint.jl * Update trig.jl * Update toint.jl * Update src/ADNLPProblems/toint.jl Co-authored-by: Tangi Migot <tangi.migot@gmail.com> * fixing Float64 issue in toint and trig problems * further changes * trig changes * review changes to toint and trig problems * fixing AD and JuMP inconsistency in toint.jl * fixing AD and JuMP incompatibility in toint.jl - 2 * Update toint.jl * Update toint.jl * Fix calculation in trigb.jl for sine terms * Apply suggestions from code review --------- Co-authored-by: Tangi Migot <tangi.migot@gmail.com>
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‎src/ADNLPProblems/toint.jl‎

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export toint
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function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
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function f(x; n = length(x))
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s = zero(T)
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for i ∈ 1:n
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ci = 1 + (i // 10)
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jmin = max(1, i - 2)
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jmax = min(n, i + 2)
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for j ∈ jmin:jmax
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aij = 5 * (1 + mod(i, 5) + mod(j, 5))
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bij = (i + j) // 10
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cj = 1 + j // 10
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s += aij * sin(bij + ci * x[i] + cj * x[j])
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end
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if iseven(n)
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half = n ÷ 2
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j1 = i + half
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if 1 <= j1 <= n && (j1 < jmin || j1 > jmax)
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aij = 5 * (1 + mod(i, 5) + mod(j1, 5))
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bij = (i + j1) // 10
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cj = 1 + j1 // 10
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s += aij * sin(bij + ci * x[i] + cj * x[j1])
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end
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j2 = i - half
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if 1 <= j2 <= n && j2 != j1 && (j2 < jmin || j2 > jmax)
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aij = 5 * (1 + mod(i, 5) + mod(j2, 5))
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bij = (i + j2) // 10
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cj = 1 + j2 // 10
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s += aij * sin(bij + ci * x[i] + cj * x[j2])
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end
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end
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end
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return s / n
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end
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x0 = fill(one(T), n)
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return ADNLPModels.ADNLPModel(f, x0, name = "toint"; kwargs...)
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end

‎src/ADNLPProblems/trig.jl‎

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export trig
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function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
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function f(x; n = length(x))
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s = zero(T)
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for i = 1:n
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s += i * (1 - cos(x[i]))
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jmin = max(1, i - 2)
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jmax = min(n, i + 2)
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for j in jmin:jmax
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aij = 5 * (1 + mod(i, 5) + mod(j, 5))
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bij = (i + j) // 10
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s += aij * sin(x[j]) + bij * cos(x[j])
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end
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if iseven(n)
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half = n ÷ 2
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j1 = i + half
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if 1 <= j1 <= n && (j1 < jmin || j1 > jmax)
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aij = 5 * (1 + mod(i, 5) + mod(j1, 5))
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bij = (i + j1) // 10
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s += aij * sin(x[j1]) + bij * cos(x[j1])
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end
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j2 = i - half
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if 1 <= j2 <= n && j2 != j1 && (j2 < jmin || j2 > jmax)
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aij = 5 * (1 + mod(i, 5) + mod(j2, 5))
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bij = (i + j2) // 10
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s += aij * sin(x[j2]) + bij * cos(x[j2])
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end
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end
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end
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return s / n
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end
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x0 = fill(one(T) / n, n)
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return ADNLPModels.ADNLPModel(f, x0, name = "trig"; kwargs...)
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end

‎src/ADNLPProblems/trigb.jl‎

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export trigb
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function trigb(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
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function f(x; n = length(x))
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s = zero(T)
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for i = 1:n
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xim = (i == 1) ? zero(T) : x[i - 1]
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xip = (i == n) ? zero(T) : x[i + 1]
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s += i * (1 - cos(x[i]) + sin(xim) - sin(xip))
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end
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return s
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end
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x0 = fill(one(T), n)
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return ADNLPModels.ADNLPModel(f, x0, name = "trigb"; kwargs...)
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end

‎src/Meta/toint.jl‎

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toint_meta = Dict(
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:nvar => 100,
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:variable_nvar => true,
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:ncon => 0,
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:variable_ncon => false,
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:minimize => true,
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:name => "toint",
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:has_equalities_only => false,
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:has_inequalities_only => false,
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:has_bounds => false,
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:has_fixed_variables => false,
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:objtype => :other,
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:contype => :unconstrained,
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:best_known_lower_bound => -Inf,
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:best_known_upper_bound => -0.8598396932382264,
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:is_feasible => true,
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:defined_everywhere => missing,
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:origin => :unknown,
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)
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get_toint_nvar(; n::Integer = default_nvar, kwargs...) = n
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get_toint_ncon(; n::Integer = default_nvar, kwargs...) = 0
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get_toint_nlin(; n::Integer = default_nvar, kwargs...) = 0
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get_toint_nnln(; n::Integer = default_nvar, kwargs...) = 0
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get_toint_nequ(; n::Integer = default_nvar, kwargs...) = 0
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get_toint_nineq(; n::Integer = default_nvar, kwargs...) = 0

‎src/Meta/trig.jl‎

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trig_meta = Dict(
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:nvar => 100,
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:variable_nvar => true,
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:ncon => 0,
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:variable_ncon => false,
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:minimize => true,
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:name => "trig",
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:has_equalities_only => false,
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:has_inequalities_only => false,
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:has_bounds => false,
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:has_fixed_variables => false,
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:objtype => :other,
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:contype => :unconstrained,
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:best_known_lower_bound => -Inf,
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:best_known_upper_bound => 61.482500487413226,
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:is_feasible => true,
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:defined_everywhere => missing,
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:origin => :unknown,
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)
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get_trig_nvar(; n::Integer = default_nvar, kwargs...) = n
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get_trig_ncon(; n::Integer = default_nvar, kwargs...) = 0
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get_trig_nlin(; n::Integer = default_nvar, kwargs...) = 0
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get_trig_nnln(; n::Integer = default_nvar, kwargs...) = 0
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get_trig_nequ(; n::Integer = default_nvar, kwargs...) = 0
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get_trig_nineq(; n::Integer = default_nvar, kwargs...) = 0

‎src/Meta/trigb.jl‎

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trigb_meta = Dict(
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:nvar => 100,
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:variable_nvar => true,
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:ncon => 0,
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:variable_ncon => false,
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:minimize => true,
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:name => "trigb",
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:has_equalities_only => false,
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:has_inequalities_only => false,
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:has_bounds => false,
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:has_fixed_variables => false,
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:objtype => :other,
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:contype => :unconstrained,
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:best_known_lower_bound => -Inf,
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:best_known_upper_bound => 2404.778982861876,
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:is_feasible => true,
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:defined_everywhere => missing,
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:origin => :unknown,
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)
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get_trigb_nvar(; n::Integer = default_nvar, kwargs...) = n
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get_trigb_ncon(; n::Integer = default_nvar, kwargs...) = 0
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get_trigb_nlin(; n::Integer = default_nvar, kwargs...) = 0
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get_trigb_nnln(; n::Integer = default_nvar, kwargs...) = 0
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get_trigb_nequ(; n::Integer = default_nvar, kwargs...) = 0
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get_trigb_nineq(; n::Integer = default_nvar, kwargs...) = 0

‎src/PureJuMP/toint.jl‎

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# Toint trigonometric function
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#
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# Problem 10 in
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# L. Luksan, C. Matonoha and J. Vlcek
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# Sparse Test Problems for Unconstrained Optimization,
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# Technical Report 1064,
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# Institute of Computer Science,
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# Academy of Science of the Czech Republic
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#
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# https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
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#
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export toint
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function toint(args...; n::Int = default_nvar, kwargs...)
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model = Model()
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@variable(model, x[i = 1:n], start = 1)
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@objective(
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model,
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Min,
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(1 / n) * sum(begin
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ci = 1 + (i // 10)
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s = zero(Float64)
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jmin = max(1, i - 2)
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jmax = min(n, i + 2)
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for j in jmin:jmax
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aij = 5 * (1 + mod(i, 5) + mod(j, 5))
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bij = (i + j) // 10
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cj = 1 + j // 10
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s += aij * sin(bij + ci * x[i] + cj * x[j])
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end
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if iseven(n)
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half = n ÷ 2
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j1 = i + half
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if 1 <= j1 <= n && (j1 < jmin || j1 > jmax)
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aij = 5 * (1 + mod(i, 5) + mod(j1, 5))
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bij = (i + j1) // 10
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cj = 1 + j1 // 10
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s += aij * sin(bij + ci * x[i] + cj * x[j1])
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end
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j2 = i - half
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if 1 <= j2 <= n && j2 != j1 && (j2 < jmin || j2 > jmax)
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aij = 5 * (1 + mod(i, 5) + mod(j2, 5))
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bij = (i + j2) // 10
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cj = 1 + j2 // 10
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s += aij * sin(bij + ci * x[i] + cj * x[j2])
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end
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end
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s
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end for i = 1:n)
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)
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return model
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end

‎src/PureJuMP/trig.jl‎

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# Another trigonometric function
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#
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# Problem 9 in
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# L. Luksan, C. Matonoha and J. Vlcek
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# Sparse Test Problems for Unconstrained Optimization,
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# Technical Report 1064,
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# Institute of Computer Science,
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# Academy of Science of the Czech Republic
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#
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# https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
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#
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export trig
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function trig(args...; n::Int = default_nvar, kwargs...)
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model = Model()
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@variable(model, x[i = 1:n], start = 1 / n)
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@objective(
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model,
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Min,
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(1 / n) * sum(
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i * (1 - cos(x[i])) +
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(
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begin
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jmin = max(1, i - 2)
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jmax = min(n, i + 2)
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s = zero(Float64)
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for j in jmin:jmax
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aij = 5 * (1 + mod(i, 5) + mod(j, 5))
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bij = (i + j) / 10
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s += aij * sin(x[j]) + bij * cos(x[j])
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end
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if iseven(n)
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half = n ÷ 2
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j1 = i + half
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if 1 <= j1 <= n && (j1 < jmin || j1 > jmax)
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aij = 5 * (1 + mod(i, 5) + mod(j1, 5))
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bij = (i + j1) / 10
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s += aij * sin(x[j1]) + bij * cos(x[j1])
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end
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j2 = i - half
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if 1 <= j2 <= n && j2 != j1 && (j2 < jmin || j2 > jmax)
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aij = 5 * (1 + mod(i, 5) + mod(j2, 5))
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bij = (i + j2) / 10
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s += aij * sin(x[j2]) + bij * cos(x[j2])
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end
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end
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s
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end
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) for i = 1:n
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)
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)
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return model
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end

‎src/PureJuMP/trigb.jl‎

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## Banded trigonometric problem
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#
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# Problem 16 in
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# L. Luksan, C. Matonoha and J. Vlcek
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# Sparse Test Problems for Unconstrained Optimization,
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# Technical Report 1064,
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# Institute of Computer Science,
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# Academy of Science of the Czech Republic
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#
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# https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
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#
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export trigb
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function trigb(args...; n::Int = default_nvar, kwargs...)
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model = Model()
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@variable(model, x[i = 1:n], start = 1)
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@objective(
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model,
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Min,
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sum(
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i *
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((1 - cos(x[i])) + ((i == 1) ? sin(0) : sin(x[i - 1])) - ((i == n) ? 0 : sin(x[i + 1])))
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for i = 1:n
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)
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)
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return model
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end

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