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Update indent in docstrings
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@bgoujaud
bgoujaud committed Dec 23, 2023
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4 changes: 2 additions & 2 deletions PEPit/examples/adaptive_methods/polyak_steps_in_distance_to_optimum.py
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Expand Up @@ -97,7 +97,7 @@ def wc_polyak_steps_in_distance_to_optimum(L, mu, gamma, wrapper="cvxpy", solver
(PEPit) Final upper bound (dual): 0.6694214876573649 and lower bound (primal example): 0.6694214876445734
(PEPit) Duality gap: absolute: 1.2791434578218741e-11 and relative: 1.91081923934451e-11
*** Example file: worst-case performance of Polyak steps ***
PEPit guarantee: ||x_1 - x_*||^2 <= 0.669421 ||x_0 - x_*||^2
PEPit guarantee: ||x_1 - x_*||^2 <= 0.669421 ||x_0 - x_*||^2
Theoretical guarantee: ||x_1 - x_*||^2 <= 0.669421 ||x_0 - x_*||^2
"""
Expand Down Expand Up @@ -142,7 +142,7 @@ def wc_polyak_steps_in_distance_to_optimum(L, mu, gamma, wrapper="cvxpy", solver
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of Polyak steps ***')
print('\tPEPit guarantee:\t\t ||x_1 - x_*||^2 <= {:.6} ||x_0 - x_*||^2 '.format(pepit_tau))
print('\tPEPit guarantee:\t ||x_1 - x_*||^2 <= {:.6} ||x_0 - x_*||^2 '.format(pepit_tau))
print('\tTheoretical guarantee:\t ||x_1 - x_*||^2 <= {:.6} ||x_0 - x_*||^2'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method (and the reference theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/adaptive_methods/polyak_steps_in_function_value.py
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Expand Up @@ -97,7 +97,7 @@ def wc_polyak_steps_in_function_value(L, mu, gamma, wrapper="cvxpy", solver=None
(PEPit) Final upper bound (dual): 0.6694214228930617 and lower bound (primal example): 0.6694214253294206
(PEPit) Duality gap: absolute: -2.4363588924103396e-09 and relative: -3.6394994247628294e-09
*** Example file: worst-case performance of Polyak steps ***
PEPit guarantee: f(x_1) - f_* <= 0.669421 (f(x_0) - f_*)
PEPit guarantee: f(x_1) - f_* <= 0.669421 (f(x_0) - f_*)
Theoretical guarantee: f(x_1) - f_* <= 0.669421 (f(x_0) - f_*)
"""
Expand Down Expand Up @@ -142,7 +142,7 @@ def wc_polyak_steps_in_function_value(L, mu, gamma, wrapper="cvxpy", solver=None
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of Polyak steps ***')
print('\tPEPit guarantee:\t\t f(x_1) - f_* <= {:.6} (f(x_0) - f_*) '.format(pepit_tau))
print('\tPEPit guarantee:\t f(x_1) - f_* <= {:.6} (f(x_0) - f_*) '.format(pepit_tau))
print('\tTheoretical guarantee:\t f(x_1) - f_* <= {:.6} (f(x_0) - f_*)'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method (and the reference theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/accelerated_proximal_gradient.py
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Expand Up @@ -95,7 +95,7 @@ def wc_accelerated_proximal_gradient(mu, L, n, wrapper="cvxpy", solver=None, ver
(PEPit) Final upper bound (dual): 0.05263158967733932 and lower bound (primal example): 0.052631584231766296
(PEPit) Duality gap: absolute: 5.445573027229589e-09 and relative: 1.0346587712901982e-07
*** Example file: worst-case performance of the Accelerated Proximal Gradient Method in function values***
PEPit guarantee: f(x_n)-f_* <= 0.0526316 ||x0 - xs||^2
PEPit guarantee: f(x_n)-f_* <= 0.0526316 ||x0 - xs||^2
Theoretical guarantee: f(x_n)-f_* <= 0.0526316 ||x0 - xs||^2
"""
Expand Down Expand Up @@ -144,7 +144,7 @@ def wc_accelerated_proximal_gradient(mu, L, n, wrapper="cvxpy", solver=None, ver
if verbose != -1:
print('*** Example file:'
' worst-case performance of the Accelerated Proximal Gradient Method in function values***')
print('\tPEPit guarantee:\t\t f(x_n)-f_* <= {:.6} ||x0 - xs||^2'.format(pepit_tau))
print('\tPEPit guarantee:\t f(x_n)-f_* <= {:.6} ||x0 - xs||^2'.format(pepit_tau))
print('\tTheoretical guarantee:\t f(x_n)-f_* <= {:.6} ||x0 - xs||^2'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method ( and the reference theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/bregman_proximal_point.py
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Expand Up @@ -82,7 +82,7 @@ def wc_bregman_proximal_point(gamma, n, wrapper="cvxpy", solver=None, verbose=1)
(PEPit) Final upper bound (dual): 0.06666666638907502 and lower bound (primal example): 0.06666666577966435
(PEPit) Duality gap: absolute: 6.094106747012162e-10 and relative: 9.1411602421417e-09
*** Example file: worst-case performance of the Bregman Proximal Point in function values ***
PEPit guarantee: F(x_n)-F_* <= 0.0666667 Dh(x_*; x_0)
PEPit guarantee: F(x_n)-F_* <= 0.0666667 Dh(x_*; x_0)
Theoretical guarantee: F(x_n)-F_* <= 0.0666667 Dh(x_*; x_0)
"""
Expand Down Expand Up @@ -124,7 +124,7 @@ def wc_bregman_proximal_point(gamma, n, wrapper="cvxpy", solver=None, verbose=1)
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the Bregman Proximal Point in function values ***')
print('\tPEPit guarantee:\t\t F(x_n)-F_* <= {:.6} Dh(x_*; x_0)'.format(pepit_tau))
print('\tPEPit guarantee:\t F(x_n)-F_* <= {:.6} Dh(x_*; x_0)'.format(pepit_tau))
print('\tTheoretical guarantee:\t F(x_n)-F_* <= {:.6} Dh(x_*; x_0)'.format(theoretical_tau))
# Return the worst-case guarantee of the evaluated method (and the upper theoretical value)
return pepit_tau, theoretical_tau
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/douglas_rachford_splitting.py
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Expand Up @@ -98,7 +98,7 @@ def wc_douglas_rachford_splitting(L, alpha, theta, n, wrapper="cvxpy", solver=No
(PEPit) Final upper bound (dual): 0.027791732322924277 and lower bound (primal example): 0.027791729871150122
(PEPit) Duality gap: absolute: 2.4517741552265715e-09 and relative: 8.821955907723812e-08
*** Example file: worst-case performance of the Douglas Rachford Splitting in function values ***
PEPit guarantee: f(y_n)-f_* <= 0.0278 ||x0 - xs||^2
PEPit guarantee: f(y_n)-f_* <= 0.0278 ||x0 - xs||^2
Theoretical guarantee: f(y_n)-f_* <= 0.0278 ||x0 - xs||^2
"""
Expand Down Expand Up @@ -147,7 +147,7 @@ def wc_douglas_rachford_splitting(L, alpha, theta, n, wrapper="cvxpy", solver=No
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the Douglas Rachford Splitting in function values ***')
print('\tPEPit guarantee:\t\t f(y_n)-f_* <= {:.3} ||x0 - xs||^2'.format(pepit_tau))
print('\tPEPit guarantee:\t f(y_n)-f_* <= {:.3} ||x0 - xs||^2'.format(pepit_tau))
if theta == 1 and alpha == 1 and L == 1 and n <= 10:
print('\tTheoretical guarantee:\t f(y_n)-f_* <= {:.3} ||x0 - xs||^2'.format(theoretical_tau))

Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/douglas_rachford_splitting_contraction.py
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Expand Up @@ -109,7 +109,7 @@ def wc_douglas_rachford_splitting_contraction(mu, L, alpha, theta, n, wrapper="c
(PEPit) Final upper bound (dual): 0.3501278016887412 and lower bound (primal example): 0.3501278029546837
(PEPit) Duality gap: absolute: -1.2659425174810224e-09 and relative: -3.6156583590274623e-09
*** Example file: worst-case performance of the Douglas-Rachford splitting in distance ***
PEPit guarantee: ||w - wp||^2 <= 0.350128 ||w0 - w0p||^2
PEPit guarantee: ||w - wp||^2 <= 0.350128 ||w0 - w0p||^2
Theoretical guarantee: ||w - wp||^2 <= 0.350128 ||w0 - w0p||^2
"""
Expand Down Expand Up @@ -158,7 +158,7 @@ def wc_douglas_rachford_splitting_contraction(mu, L, alpha, theta, n, wrapper="c
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the Douglas-Rachford splitting in distance ***')
print('\tPEPit guarantee:\t\t ||w - wp||^2 <= {:.6} ||w0 - w0p||^2'.format(pepit_tau))
print('\tPEPit guarantee:\t ||w - wp||^2 <= {:.6} ||w0 - w0p||^2'.format(pepit_tau))
if theta == 1:
print('\tTheoretical guarantee:\t ||w - wp||^2 <= {:.6} ||w0 - w0p||^2'.format(theoretical_tau))

Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/frank_wolfe.py
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Expand Up @@ -93,7 +93,7 @@ def wc_frank_wolfe(L, D, n, wrapper="cvxpy", solver=None, verbose=1):
(PEPit) Final upper bound (dual): 0.07828954284798424 and lower bound (primal example): 0.07828953904645822
(PEPit) Duality gap: absolute: 3.801526024527213e-09 and relative: 4.855726666459652e-08
*** Example file: worst-case performance of the Conditional Gradient (Frank-Wolfe) in function value ***
PEPit guarantee: f(x_n)-f_* <= 0.0782895 ||x0 - xs||^2
PEPit guarantee: f(x_n)-f_* <= 0.0782895 ||x0 - xs||^2
Theoretical guarantee: f(x_n)-f_* <= 0.166667 ||x0 - xs||^2
"""
Expand Down Expand Up @@ -141,7 +141,7 @@ def wc_frank_wolfe(L, D, n, wrapper="cvxpy", solver=None, verbose=1):
if verbose != -1:
print('*** Example file:'
' worst-case performance of the Conditional Gradient (Frank-Wolfe) in function value ***')
print('\tPEPit guarantee:\t\t f(x_n)-f_* <= {:.6} ||x0 - xs||^2'.format(pepit_tau))
print('\tPEPit guarantee:\t f(x_n)-f_* <= {:.6} ||x0 - xs||^2'.format(pepit_tau))
print('\tTheoretical guarantee:\t f(x_n)-f_* <= {:.6} ||x0 - xs||^2'.format(theoretical_tau))
# Return the worst-case guarantee of the evaluated method (and the upper theoretical value)
return pepit_tau, theoretical_tau
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/improved_interior_algorithm.py
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Expand Up @@ -102,7 +102,7 @@ def wc_improved_interior_algorithm(L, mu, c, lam, n, wrapper="cvxpy", solver=Non
(PEPit) Final upper bound (dual): 0.06807717277007506 and lower bound (primal example): 0.06807717876241919
(PEPit) Duality gap: absolute: -5.992344120908655e-09 and relative: -8.802280338057462e-08
*** Example file: worst-case performance of the Improved interior gradient algorithm in function values ***
PEPit guarantee: F(x_n)-F_* <= 0.0680772 (c * Dh(xs;x0) + f1(x0) - F_*)
PEPit guarantee: F(x_n)-F_* <= 0.0680772 (c * Dh(xs;x0) + f1(x0) - F_*)
Theoretical guarantee: F(x_n)-F_* <= 0.111111 (c * Dh(xs;x0) + f1(x0) - F_*)
"""
Expand Down Expand Up @@ -163,7 +163,7 @@ def wc_improved_interior_algorithm(L, mu, c, lam, n, wrapper="cvxpy", solver=Non
if verbose != -1:
print('*** Example file:'
' worst-case performance of the Improved interior gradient algorithm in function values ***')
print('\tPEPit guarantee:\t\t F(x_n)-F_* <= {:.6} (c * Dh(xs;x0) + f1(x0) - F_*)'.format(pepit_tau))
print('\tPEPit guarantee:\t F(x_n)-F_* <= {:.6} (c * Dh(xs;x0) + f1(x0) - F_*)'.format(pepit_tau))
print('\tTheoretical guarantee:\t F(x_n)-F_* <= {:.6} (c * Dh(xs;x0) + f1(x0) - F_*)'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method (and the upper theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/no_lips_in_bregman_divergence.py
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Expand Up @@ -101,7 +101,7 @@ def wc_no_lips_in_bregman_divergence(L, gamma, n, wrapper="cvxpy", solver=None,
(PEPit) Final upper bound (dual): 0.022222222222206895 and lower bound (primal example): 0.022222222222201146
(PEPit) Duality gap: absolute: 5.748873599387139e-15 and relative: 2.586993119726666e-13
*** Example file: worst-case performance of the NoLips_2 in Bregman divergence ***
PEPit guarantee: min_t Dh(x_(t-1); x_t) <= 0.0222222 Dh(x_*; x_0)
PEPit guarantee: min_t Dh(x_(t-1); x_t) <= 0.0222222 Dh(x_*; x_0)
Theoretical guarantee: min_t Dh(x_(t-1); x_t) <= 0.0222222 Dh(x_*; x_0)
"""
Expand Down Expand Up @@ -156,7 +156,7 @@ def wc_no_lips_in_bregman_divergence(L, gamma, n, wrapper="cvxpy", solver=None,
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the NoLips_2 in Bregman divergence ***')
print('\tPEPit guarantee:\t\t min_t Dh(x_(t-1); x_t) <= {:.6} Dh(x_*; x_0)'.format(pepit_tau))
print('\tPEPit guarantee:\t min_t Dh(x_(t-1); x_t) <= {:.6} Dh(x_*; x_0)'.format(pepit_tau))
print('\tTheoretical guarantee:\t min_t Dh(x_(t-1); x_t) <= {:.6} Dh(x_*; x_0)'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method (and the upper theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/no_lips_in_function_value.py
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Expand Up @@ -103,7 +103,7 @@ def wc_no_lips_in_function_value(L, gamma, n, wrapper="cvxpy", solver=None, verb
(PEPit) Final upper bound (dual): 0.666666666662425 and lower bound (primal example): 0.6666666666481619
(PEPit) Duality gap: absolute: 1.4263146219661849e-11 and relative: 2.139471933008663e-11
*** Example file: worst-case performance of the NoLips in function values ***
PEPit guarantee: F(x_n) - F_* <= 0.666667 Dh(x_*; x_0)
PEPit guarantee: F(x_n) - F_* <= 0.666667 Dh(x_*; x_0)
Theoretical guarantee: F(x_n) - F_* <= 0.666667 Dh(x_*; x_0)
"""
Expand Down Expand Up @@ -155,7 +155,7 @@ def wc_no_lips_in_function_value(L, gamma, n, wrapper="cvxpy", solver=None, verb
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the NoLips in function values ***')
print('\tPEPit guarantee:\t\t F(x_n) - F_* <= {:.6} Dh(x_*; x_0)'.format(pepit_tau))
print('\tPEPit guarantee:\t F(x_n) - F_* <= {:.6} Dh(x_*; x_0)'.format(pepit_tau))
print('\tTheoretical guarantee:\t F(x_n) - F_* <= {:.6} Dh(x_*; x_0)'.format(theoretical_tau))
# Return the worst-case guarantee of the evaluated method (and the upper theoretical value)
return pepit_tau, theoretical_tau
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/proximal_gradient.py
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Expand Up @@ -105,7 +105,7 @@ def wc_proximal_gradient(L, mu, gamma, n, wrapper="cvxpy", solver=None, verbose=
(PEPit) Final upper bound (dual): 0.6561000458035535 and lower bound (primal example): 0.6561000457701127
(PEPit) Duality gap: absolute: 3.3440805680129415e-11 and relative: 5.096906469634138e-11
*** Example file: worst-case performance of the Proximal Gradient Method in function values***
PEPit guarantee: ||x_n - x_*||^2 <= 0.6561 ||x0 - xs||^2
PEPit guarantee: ||x_n - x_*||^2 <= 0.6561 ||x0 - xs||^2
Theoretical guarantee: ||x_n - x_*||^2 <= 0.6561 ||x0 - xs||^2
"""
Expand Down Expand Up @@ -146,7 +146,7 @@ def wc_proximal_gradient(L, mu, gamma, n, wrapper="cvxpy", solver=None, verbose=
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the Proximal Gradient Method in function values***')
print('\tPEPit guarantee:\t\t ||x_n - x_*||^2 <= {:.6} ||x0 - xs||^2'.format(pepit_tau))
print('\tPEPit guarantee:\t ||x_n - x_*||^2 <= {:.6} ||x0 - xs||^2'.format(pepit_tau))
print('\tTheoretical guarantee:\t ||x_n - x_*||^2 <= {:.6} ||x0 - xs||^2'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method ( and the reference theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/composite_convex_minimization/three_operator_splitting.py
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Expand Up @@ -98,7 +98,7 @@ def wc_three_operator_splitting(mu1, L1, L3, alpha, theta, n, wrapper="cvxpy", s
(PEPit) Final upper bound (dual): 0.475452328074928 and lower bound (primal example): 0.4754523280192519
(PEPit) Duality gap: absolute: 5.5676074861565894e-11 and relative: 1.1710127720588522e-10
*** Example file: worst-case performance of the Three Operator Splitting in distance ***
PEPit guarantee: ||w^2_n - w^1_n||^2 <= 0.475452 ||x0 - ws||^2
PEPit guarantee: ||w^2_n - w^1_n||^2 <= 0.475452 ||x0 - ws||^2
"""

Expand Down Expand Up @@ -146,7 +146,7 @@ def wc_three_operator_splitting(mu1, L1, L3, alpha, theta, n, wrapper="cvxpy", s
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the Three Operator Splitting in distance ***')
print('\tPEPit guarantee:\t\t ||w^2_n - w^1_n||^2 <= {:.6} ||x0 - ws||^2'.format(pepit_tau))
print('\tPEPit guarantee:\t ||w^2_n - w^1_n||^2 <= {:.6} ||x0 - ws||^2'.format(pepit_tau))

# Return the worst-case guarantee of the evaluated method (and the upper theoretical value)
return pepit_tau, theoretical_tau
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/continuous_time_models/accelerated_gradient_flow_convex.py
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Expand Up @@ -88,7 +88,7 @@ def wc_accelerated_gradient_flow_convex(t, wrapper="cvxpy", solver=None, verbose
(PEPit) Final upper bound (dual): 0.0 and lower bound (primal example): -4.440892098500626e-15
(PEPit) Duality gap: absolute: 4.440892098500626e-15 and relative: -1.0
*** Example file: worst-case performance of an accelerated gradient flow ***
PEPit guarantee: d/dt V(X_t,t) <= 0.0
PEPit guarantee: d/dt V(X_t,t) <= 0.0
Theoretical guarantee: d/dt V(X_t) <= 0.0
"""
Expand Down Expand Up @@ -128,7 +128,7 @@ def wc_accelerated_gradient_flow_convex(t, wrapper="cvxpy", solver=None, verbose
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of an accelerated gradient flow ***')
print('\tPEPit guarantee:\t\t d/dt V(X_t,t) <= {:.6}'.format(pepit_tau))
print('\tPEPit guarantee:\t d/dt V(X_t,t) <= {:.6}'.format(pepit_tau))
print('\tTheoretical guarantee:\t d/dt V(X_t) <= {:.6}'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method (and the reference theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/continuous_time_models/accelerated_gradient_flow_strongly_convex.py
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Expand Up @@ -103,7 +103,7 @@ def wc_accelerated_gradient_flow_strongly_convex(mu, psd=True, wrapper="cvxpy",
(PEPit) Final upper bound (dual): -0.31622777578996025 and lower bound (primal example): -0.31622777856752843
(PEPit) Duality gap: absolute: 2.7775681754604875e-09 and relative: -8.783441442249373e-09
*** Example file: worst-case performance of an accelerated gradient flow ***
PEPit guarantee: d/dt V(X_t,t) <= -0.316228 V(X_t,t)
PEPit guarantee: d/dt V(X_t,t) <= -0.316228 V(X_t,t)
Theoretical guarantee: d/dt V(X_t) <= -0.316228 V(X_t,t)
"""
Expand Down Expand Up @@ -155,7 +155,7 @@ def wc_accelerated_gradient_flow_strongly_convex(mu, psd=True, wrapper="cvxpy",
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of an accelerated gradient flow ***')
print('\tPEPit guarantee:\t\t d/dt V(X_t,t) <= {:.6} V(X_t,t)'.format(pepit_tau))
print('\tPEPit guarantee:\t d/dt V(X_t,t) <= {:.6} V(X_t,t)'.format(pepit_tau))
print('\tTheoretical guarantee:\t d/dt V(X_t) <= {:.6} V(X_t,t)'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method (and the reference theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/continuous_time_models/gradient_flow_convex.py
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Expand Up @@ -88,7 +88,7 @@ def wc_gradient_flow_convex(t, wrapper="cvxpy", solver=None, verbose=1):
(PEPit) Final upper bound (dual): 0.0 and lower bound (primal example): 2.1751469748629293e-09
(PEPit) Duality gap: absolute: -2.1751469748629293e-09 and relative: -1.0
*** Example file: worst-case performance of the gradient flow ***
PEPit guarantee: d/dt V(X_t) <= 0.0
PEPit guarantee: d/dt V(X_t) <= 0.0
Theoretical guarantee: d/dt V(X_t) <= 0.0
"""
Expand Down Expand Up @@ -127,7 +127,7 @@ def wc_gradient_flow_convex(t, wrapper="cvxpy", solver=None, verbose=1):
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the gradient flow ***')
print('\tPEPit guarantee:\t\t d/dt V(X_t) <= {:.6}'.format(pepit_tau))
print('\tPEPit guarantee:\t d/dt V(X_t) <= {:.6}'.format(pepit_tau))
print('\tTheoretical guarantee:\t d/dt V(X_t) <= {:.6}'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method (and the reference theoretical value)
Expand Down
4 changes: 2 additions & 2 deletions PEPit/examples/continuous_time_models/gradient_flow_strongly_convex.py
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Expand Up @@ -84,7 +84,7 @@ def wc_gradient_flow_strongly_convex(mu, wrapper="cvxpy", solver=None, verbose=1
(PEPit) Final upper bound (dual): -0.20000002574229303 and lower bound (primal example): -0.20000002010543685
(PEPit) Duality gap: absolute: -5.636856176272076e-09 and relative: 2.8184278048074267e-08
*** Example file: worst-case performance of the gradient flow ***
PEPit guarantee: d/dt[f(X_t)-f_*] <= -0.2 (f(X_t) - f(x_*))
PEPit guarantee: d/dt[f(X_t)-f_*] <= -0.2 (f(X_t) - f(x_*))
Theoretical guarantee: d/dt[f(X_t)-f_*] <= -0.2 (f(X_t) - f(x_*))
"""
Expand Down Expand Up @@ -128,7 +128,7 @@ def wc_gradient_flow_strongly_convex(mu, wrapper="cvxpy", solver=None, verbose=1
# Print conclusion if required
if verbose != -1:
print('*** Example file: worst-case performance of the gradient flow ***')
print('\tPEPit guarantee:\t\t d/dt[f(X_t)-f_*] <= {:.6} (f(X_t) - f(x_*))'.format(pepit_tau))
print('\tPEPit guarantee:\t d/dt[f(X_t)-f_*] <= {:.6} (f(X_t) - f(x_*))'.format(pepit_tau))
print('\tTheoretical guarantee:\t d/dt[f(X_t)-f_*] <= {:.6} (f(X_t) - f(x_*))'.format(theoretical_tau))

# Return the worst-case guarantee of the evaluated method (and the reference theoretical value)
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