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elvis
2023-11-30 15:24:11 +01:00
parent 5161464087
commit 65c8842e83
2 changed files with 37 additions and 37 deletions
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62
11-09/NWTN.jl
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@ -34,10 +34,10 @@ function NWTN(f;
# #
# saves the point in lastx, the gradient in lastg, the Hessian in lasth, # saves the point in lastx, the gradient in lastg, the Hessian in lasth,
# and increases feval # and increases feval
lastx = x + alpha * d lastx = x + alpha * d
phi, lastg, lastH = f(lastx) phi, lastg, lastH = f(lastx)
if Plotf > 2 if Plotf > 2
if fStar > - Inf if fStar > - Inf
push!(gap, (phi - fStar) / max(abs(fStar), 1)) push!(gap, (phi - fStar) / max(abs(fStar), 1))
@ -56,7 +56,7 @@ function NWTN(f;
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
function ArmijoWolfeLS(phi0, phip0, as, m1, m2, tau) function ArmijoWolfeLS(phi0, phip0, as, m1, m2, tau)
# performs an Armijo-Wolfe Line Search. # performs an Armijo-Wolfe Line Search.
# #
@ -70,12 +70,12 @@ function NWTN(f;
# Wolfe condition is used # Wolfe condition is used
# #
# returns the optimal step and the optimal f-value # returns the optimal step and the optimal f-value
lsiter = 1 # count iterations of first phase lsiter = 1 # count iterations of first phase
local phips, phia local phips, phia
while feval ≤ MaxFeval while feval ≤ MaxFeval
phia, phips = f2phi(as, true) phia, phips = f2phi(as, true)
if (phia ≤ phi0 + m1 * as * phip0) && (abs(phips) ≤ - m2 * phip0) if (phia ≤ phi0 + m1 * as * phip0) && (abs(phips) ≤ - m2 * phip0)
if printing if printing
@printf(" %2d", lsiter) @printf(" %2d", lsiter)
@ -88,29 +88,29 @@ function NWTN(f;
end end
as = as / tau as = as / tau
lsiter += 1 lsiter += 1
end end
if printing if printing
@printf(" %2d ", lsiter) @printf(" %2d ", lsiter)
end end
lsiter = 1 # count iterations of second phase lsiter = 1 # count iterations of second phase
am = 0 am = 0
a = as a = as
phipm = phip0 phipm = phip0
while (feval ≤ MaxFeval ) && (as - am) > mina && (phips > 1e-12) while (feval ≤ MaxFeval ) && (as - am) > mina && (phips > 1e-12)
# compute the new value by safeguarded quadratic interpolation # compute the new value by safeguarded quadratic interpolation
a = (am * phips - as * phipm) / (phips - phipm) a = (am * phips - as * phipm) / (phips - phipm)
a = max(am + ( as - am ) * sfgrd, min(as - ( as - am ) * sfgrd, a)) a = max(am + ( as - am ) * sfgrd, min(as - ( as - am ) * sfgrd, a))
# compute phi(a) # compute phi(a)
phia, phip = f2phi(a, true) phia, phip = f2phi(a, true)
if (phia ≤ phi0 + m1 * a * phip0) && (abs(phip) ≤ -m2 * phip0) if (phia ≤ phi0 + m1 * a * phip0) && (abs(phip) ≤ -m2 * phip0)
break # Armijo + strong Wolfe satisfied, we are done break # Armijo + strong Wolfe satisfied, we are done
end end
# restrict the interval based on sign of the derivative in a # restrict the interval based on sign of the derivative in a
if phip < 0 if phip < 0
am = a am = a
@ -143,7 +143,7 @@ function NWTN(f;
# m1 is satisfied # m1 is satisfied
# #
# returns the optimal step and the optimal f-value # returns the optimal step and the optimal f-value
lsiter = 1 # count ls iterations lsiter = 1 # count ls iterations
while feval ≤ MaxFeval && as > mina while feval ≤ MaxFeval && as > mina
phia, _ = f2phi(as) phia, _ = f2phi(as)
@ -160,7 +160,7 @@ function NWTN(f;
return (as, phia) return (as, phia)
end end
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
@ -227,7 +227,7 @@ function NWTN(f;
# "global" variables- - - - - - - - - - - - - - - - - - - - - - - - - - - - # "global" variables- - - - - - - - - - - - - - - - - - - - - - - - - - - -
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
lastx = zeros(n) # last point visited in the line search lastx = zeros(n) # last point visited in the line search
lastg = zeros(n) # gradient of lastx lastg = zeros(n) # gradient of lastx
lastH = zeros(n, n) # Hessian of lastx lastH = zeros(n, n) # Hessian of lastx
@ -235,7 +235,7 @@ function NWTN(f;
feval = 0 # f() evaluations count ("common" with LSs) feval = 0 # f() evaluations count ("common" with LSs)
status = "error" status = "error"
# initializations - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # initializations - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
@ -254,7 +254,7 @@ function NWTN(f;
@printf("\n\n") @printf("\n\n")
end end
v, _ = f2phi(0) v, _ = f2phi(0)
ng = norm(lastg) ng = norm(lastg)
if eps < 0 if eps < 0
@ -269,7 +269,7 @@ function NWTN(f;
while true while true
# output statistics - - - - - - - - - - - - - - - - - - - - - - - - - - # output statistics - - - - - - - - - - - - - - - - - - - - - - - - - -
if fStar > -Inf if fStar > -Inf
gapk = (v - fStar) / max(abs(fStar), 1) gapk = (v - fStar) / max(abs(fStar), 1)
@ -282,7 +282,7 @@ function NWTN(f;
end end
end end
prevv = v prevv = v
if Plotf > 1 if Plotf > 1
if Plotf ≥ 2 if Plotf ≥ 2
push!(gap, gapk) push!(gap, gapk)
@ -292,7 +292,7 @@ function NWTN(f;
if printing if printing
@printf("%4d\t%1.8e\t\t%1.4e", feval, v, ng) @printf("%4d\t%1.8e\t\t%1.4e", feval, v, ng)
end end
if Plotf > 1 if Plotf > 1
if Plotf ≥ 2 if Plotf ≥ 2
push!(gap, v) push!(gap, v)
@ -306,12 +306,12 @@ function NWTN(f;
status = "optimal" status = "optimal"
break break
end end
if feval > MaxFeval if feval > MaxFeval
status = "stopped" status = "stopped"
break break
end end
# compute Newton's direction- - - - - - - - - - - - - - - - - - - - - - # compute Newton's direction- - - - - - - - - - - - - - - - - - - - - -
lambdan = eigmin(lastH) # smallest eigenvalue lambdan = eigmin(lastH) # smallest eigenvalue
@ -327,45 +327,45 @@ function NWTN(f;
end end
d = -lastH \ lastg d = -lastH \ lastg
phip0 = lastg' * d phip0 = lastg' * d
# compute step size - - - - - - - - - - - - - - - - - - - - - - - - - - # compute step size - - - - - - - - - - - - - - - - - - - - - - - - - -
# in Newton's method, the default initial stepsize is 1 # in Newton's method, the default initial stepsize is 1
if AWLS if AWLS
a, v = ArmijoWolfeLS(v, phip0, 1, m1, m2, tau) a, v = ArmijoWolfeLS(v, phip0, 1, m1, m2, tau)
else else
a, v = BacktrackingLS(v, phip0, 1, m1, tau) a, v = BacktrackingLS(v, phip0, 1, m1, tau)
end end
# output statistics - - - - - - - - - - - - - - - - - - - - - - - - - - # output statistics - - - - - - - - - - - - - - - - - - - - - - - - - -
if printing if printing
@printf("\t%1.2e", a) @printf("\t%1.2e", a)
@printf("\n") @printf("\n")
end end
if a ≤ mina if a ≤ mina
status = "error" status = "error"
break break
end end
if v ≤ MInf if v ≤ MInf
status = "unbounded" status = "unbounded"
break break
end end
# compute new point - - - - - - - - - - - - - - - - - - - - - - - - - - # compute new point - - - - - - - - - - - - - - - - - - - - - - - - - -
# possibly plot the trajectory # possibly plot the trajectory
if n == 2 && Plotf == 1 if n == 2 && Plotf == 1
PXY = hcat(PXY, hcat(x, lastx)) PXY = hcat(PXY, hcat(x, lastx))
end end
x = lastx x = lastx
ng = norm(lastg) ng = norm(lastg)
# iterate - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # iterate - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
if Interactive if Interactive
readline() readline()
end end
@ -383,4 +383,4 @@ function NWTN(f;
# end of main loop- - - - - - - - - - - - - - - - - - - - - - - - - - - - - # end of main loop- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
return (x, status) return (x, status)
end end

12
11-09/TestFunctions/TestFunctions.jl
View File

@ -307,16 +307,16 @@ function lasso(x::Union{Nothing, AbstractVecOrMat})
if isnothing(x) # informative call if isnothing(x) # informative call
v = ( 2 - 1/3 )^2 + 10/9 # optimal solution [ 1/9 , 0 ] v = ( 2 - 1/3 )^2 + 10/9 # optimal solution [ 1/9 , 0 ]
return (v, [0, 0]) return (v, [0., 0.], nothing)
else else
v = ( 3 * x( 1 ) + 2 * x( 2 ) - 2 )^2 + v = (3 * x[1] + 2 * x[2] - 2)^2 +
10 * ( abs( x( 1 ) ) + abs( x( 2 ) ) ) # f(x) 10 * (abs(x[1]) + abs(x[2])) # f(x)
g = zeros(2) g = zeros(2)
g[1] = 18 * x[1] + 12 * x[2] - 12 + 10 * sign( x[1] ) g[1] = 18 * x[1] + 12 * x[2] - 12 + 10 * sign(x[1])
g[2] = 12 * x[1] + 8 * x[2] - 8 + 10 * sign( x[2] ) g[2] = 12 * x[1] + 8 * x[2] - 8 + 10 * sign(x[2])
return (v, g) return (v, g, nothing)
end end
end # lasso end # lasso