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HZ: avoid convergence if bisected #174

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HZ: avoid convergence if bisected #174

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74 changes: 40 additions & 34 deletions src/hagerzhang.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -203,10 +203,10 @@ function (ls::HagerZhang)(ϕ, ϕdϕ,
else
# We'll still going downhill, expand the interval and try again.
# Reaching this branch means that dphi_c < 0 and phi_c <= phi_0 + ϵ_k
# So cold = c has a lower objective than phi_0 up to epsilon.
# So cold = c has a lower objective than phi_0 up to epsilon.
# This makes it a viable step to return if bracketing fails.

# Bracketing can fail if no cold < c <= alphamax can be found with finite phi_c and dphi_c.
# Bracketing can fail if no cold < c <= alphamax can be found with finite phi_c and dphi_c.
# Going back to the loop with c = cold will only result in infinite cycling.
# So returning (cold, phi_cold) and exiting the line search is the best move.
cold = c
Expand Down Expand Up @@ -266,42 +266,47 @@ function (ls::HagerZhang)(ϕ, ϕdϕ,
mayterminate[] = false # reset in case another initial guess is used next
return a, values[ia] # lsr.value[ia]
end
iswolfe, iA, iB = secant2!(ϕdϕ, alphas, values, slopes, ia, ib, phi_lim, delta, sigma, display)
iswolfe, iA, iB, bisected = secant2!(ϕdϕ, alphas, values, slopes, ia, ib, phi_lim, delta, sigma, display)
if iswolfe
mayterminate[] = false # reset in case another initial guess is used next
return alphas[iA], values[iA] # lsr.value[iA]
end
A = alphas[iA]
B = alphas[iB]
@assert B > A
if B - A < gamma * (b - a)
if display & LINESEARCH > 0
println("Linesearch: secant succeeded")
end
if nextfloat(values[ia]) >= values[ib] && nextfloat(values[iA]) >= values[iB]
# It's so flat, secant didn't do anything useful, time to quit
if !bisected
if B - A < gamma * (b - a)
if display & LINESEARCH > 0
println("Linesearch: secant suggests it's flat")
println("Linesearch: secant succeeded")
end
mayterminate[] = false # reset in case another initial guess is used next
return A, values[iA]
if nextfloat(values[ia]) >= values[ib] && nextfloat(values[iA]) >= values[iB]
# It's so flat, secant didn't do anything useful, time to quit
if display & LINESEARCH > 0
println("Linesearch: secant suggests it's flat")
end
mayterminate[] = false # reset in case another initial guess is used next
return A, values[iA]
end
ia = iA
ib = iB
else
# Secant is converging too slowly, use bisection
if display & LINESEARCH > 0
println("Linesearch: secant failed, using bisection")
end
c = (A + B) / convert(T, 2)

phi_c, dphi_c = ϕdϕ(c)
@assert isfinite(phi_c) && isfinite(dphi_c)
push!(alphas, c)
push!(values, phi_c)
push!(slopes, dphi_c)

ia, ib = update!(ϕdϕ, alphas, values, slopes, iA, iB, length(alphas), phi_lim, display)
end
else
ia = iA
ib = iB
else
# Secant is converging too slowly, use bisection
if display & LINESEARCH > 0
println("Linesearch: secant failed, using bisection")
end
c = (A + B) / convert(T, 2)

phi_c, dphi_c = ϕdϕ(c)
@assert isfinite(phi_c) && isfinite(dphi_c)
push!(alphas, c)
push!(values, phi_c)
push!(slopes, dphi_c)

ia, ib = update!(ϕdϕ, alphas, values, slopes, iA, iB, length(alphas), phi_lim, display)
end
iter += 1
end
Expand Down Expand Up @@ -373,14 +378,15 @@ function secant2!(ϕdϕ,
push!(slopes, dphi_c)

ic = length(alphas)
bisected = false
if satisfies_wolfe(c, phi_c, dphi_c, phi_0, dphi_0, phi_lim, delta, sigma)
if display & SECANT2 > 0
println("secant2: first c satisfied Wolfe conditions")
end
return true, ic, ic
return true, ic, ic, bisected
end

iA, iB = update!(ϕdϕ, alphas, values, slopes, ia, ib, ic, phi_lim, display)
iA, iB, bisected = update!(ϕdϕ, alphas, values, slopes, ia, ib, ic, phi_lim, display)
if display & SECANT2 > 0
println("secant2: iA = ", iA, ", iB = ", iB, ", ic = ", ic)
end
Expand Down Expand Up @@ -412,14 +418,14 @@ function secant2!(ϕdϕ,
if display & SECANT2 > 0
println("secant2: second c satisfied Wolfe conditions")
end
return true, ic, ic
return true, ic, ic, bisected
end
iA, iB = update!(ϕdϕ, alphas, values, slopes, iA, iB, ic, phi_lim, display)
end
if display & SECANT2 > 0
println("secant2 output: a = ", alphas[iA], ", b = ", alphas[iB])
end
return false, iA, iB
return false, iA, iB, bisected
end

# HZ, stages U0-U3
Expand Down Expand Up @@ -457,22 +463,22 @@ function update!(ϕdϕ,
", dphi_c = ", dphi_c)
end
if c < a || c > b
return ia, ib #, 0, 0 # it's out of the bracketing interval
return ia, ib, false #, 0, 0 # it's out of the bracketing interval
end
if dphi_c >= zeroT
return ia, ic #, 0, 0 # replace b with a closer point
return ia, ic, false #, 0, 0 # replace b with a closer point
end
# We know dphi_c < 0. However, phi may not be monotonic between a
# and c, so check that the value is also smaller than phi_0. (It's
# more dangerous to replace a than b, since we're leaving the
# secure environment of alpha=0; that's why we didn't check this
# above.)
if phi_c <= phi_lim
return ic, ib#, 0, 0 # replace a
return ic, ib, false#, 0, 0 # replace a
end
# phi_c is bigger than phi_0, which implies that the minimum
# lies between a and c. Find it via bisection.
return bisect!(ϕdϕ, alphas, values, slopes, ia, ic, phi_lim, display)
return (bisect!(ϕdϕ, alphas, values, slopes, ia, ic, phi_lim, display)..., true)
end

# HZ, stage U3 (with theta=0.5)
Expand Down
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