Use citations instead of links

Author: avik-pal

src/dfsane.jl

@@ -6,9 +6,7 @@
 
 A low-overhead and allocation-free implementation of the df-sane method for solving large-scale nonlinear
 systems of equations. For in depth information about all the parameters and the algorithm,
-see the paper: [W LaCruz, JM Martinez, and M Raydan (2006), Spectral Residual Method without
-Gradient Information for Solving Large-Scale Nonlinear Systems of Equations, Mathematics of
-Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_Spectral_Residual_Method_without_Gradient_Information_for_Solving_Large-Scale_Nonlinear_Systems_of_Equations)
+see the paper [1].
 
 ### Keyword Arguments
 
@@ -40,6 +38,12 @@ Computation, 75, 1429-1448.](https://www.researchgate.net/publication/220576479_
     ``fn_1 / n^2``.
   - `max_inner_iterations`: the maximum number of iterations allowed for the inner loop of the
     algorithm. Defaults to `100`.
+
+### References
+
+[1] W LaCruz, JM Martinez, and M Raydan (2006), Spectral Residual Method without Gradient
+Information for Solving Large-Scale Nonlinear Systems of Equations, Mathematics of
+Computation, 75, 1429-1448.
 """
 @kwdef @concrete struct DFSane <: AbstractNonlinearSolveAlgorithm
     σ_min = 1e-10

src/trustRegion.jl

@@ -1,34 +1,36 @@
 """
     RadiusUpdateSchemes
 
-`RadiusUpdateSchemes` is the standard enum interface for different types of radius update schemes
-implemented in the Trust Region method. These schemes specify how the radius of the so-called trust region
-is updated after each iteration of the algorithm. The specific role and caveats associated with each
-scheme are provided below.
+`RadiusUpdateSchemes` is the standard enum interface for different types of radius update
+schemes implemented in the Trust Region method. These schemes specify how the radius of the
+so-called trust region is updated after each iteration of the algorithm. The specific role
+and caveats associated with each scheme are provided below.
 
 ## Using `RadiusUpdateSchemes`
 
-`RadiusUpdateSchemes` uses the standard EnumX interface (https://github.com/fredrikekre/EnumX.jl),
-and hence inherits all properties of being an EnumX, including the type of each constituent enum
-states as `RadiusUpdateSchemes.T`. Simply put the desired scheme as follows:
+`RadiusUpdateSchemes` uses the standard
+[EnumX Interface](https://github.com/fredrikekre/EnumX.jl), and hence inherits all
+properties of being an EnumX, including the type of each constituent enum states as
+`RadiusUpdateSchemes.T`. Simply put the desired scheme as follows:
 `TrustRegion(radius_update_scheme = your desired update scheme)`. For example,
 `sol = solve(prob, alg=TrustRegion(radius_update_scheme = RadiusUpdateSchemes.Hei))`.
 """
 @enumx RadiusUpdateSchemes begin
     """
         RadiusUpdateSchemes.Simple
 
-    The simple or conventional radius update scheme. This scheme is chosen by default
-    and follows the conventional approach to update the trust region radius, i.e. if the
-    trial step is accepted it increases the radius by a fixed factor (bounded by a maximum radius)
+    The simple or conventional radius update scheme. This scheme is chosen by default and
+    follows the conventional approach to update the trust region radius, i.e. if the trial
+    step is accepted it increases the radius by a fixed factor (bounded by a maximum radius)
     and if the trial step is rejected, it shrinks the radius by a fixed factor.
     """
     Simple
 
     """
         RadiusUpdateSchemes.NLsolve
 
-    The same updating scheme as in NLsolve's (https://github.com/JuliaNLSolvers/NLsolve.jl) trust region dogleg implementation.
+    The same updating scheme as in NLsolve's (https://github.com/JuliaNLSolvers/NLsolve.jl)
+    trust region dogleg implementation.
     """
     NLsolve
 
@@ -42,40 +44,57 @@ states as `RadiusUpdateSchemes.T`. Simply put the desired scheme as follows:
     """
         RadiusUpdateSchemes.Hei
 
-    This scheme is proposed by [Hei, L.] (https://www.jstor.org/stable/43693061). The trust region radius
-    depends on the size (norm) of the current step size. The hypothesis is to let the radius converge to zero
-    as the iterations progress, which is more reliable and robust for ill-conditioned as well as degenerate
-    problems.
+    This scheme is proposed by Hei, L. [1]. The trust region radius depends on the size
+    (norm) of the current step size. The hypothesis is to let the radius converge to zero as
+    the iterations progress, which is more reliable and robust for ill-conditioned as well
+    as degenerate problems.
+
+    [1] Hei, Long. "A self-adaptive trust region algorithm." Journal of Computational
+    Mathematics (2003): 229-236.
     """
     Hei
 
     """
         RadiusUpdateSchemes.Yuan
 
-    This scheme is proposed by [Yuan, Y.] (https://www.researchgate.net/publication/249011466_A_new_trust_region_algorithm_with_trust_region_radius_converging_to_zero).
-    Similar to Hei's scheme, the trust region is updated in a way so that it converges to zero, however here,
-    the radius depends on the size (norm) of the current gradient of the objective (merit) function. The hypothesis
-    is that the step size is bounded by the gradient size, so it makes sense to let the radius depend on the gradient.
+    This scheme is proposed by Yuan, Y [1]. Similar to Hei's scheme, the trust region is
+    updated in a way so that it converges to zero, however here, the radius depends on the
+    size (norm) of the current gradient of the objective (merit) function. The hypothesis is
+    that the step size is bounded by the gradient size, so it makes sense to let the radius
+    depend on the gradient.
+
+    [1] Fan, Jinyan, Jianyu Pan, and Hongyan Song. "A retrospective trust region algorithm
+    with trust region converging to zero." Journal of Computational Mathematics 34.4 (2016):
+    421-436.
     """
     Yuan
 
     """
         RadiusUpdateSchemes.Bastin
 
-    This scheme is proposed by [Bastin, et al.] (https://www.researchgate.net/publication/225100660_A_retrospective_trust-region_method_for_unconstrained_optimization).
-    The scheme is called a retrospective update scheme as it uses the model function at the current
-    iteration to compute the ratio of the actual reduction and the predicted reduction in the previous
-    trial step, and use this ratio to update the trust region radius. The hypothesis is to exploit the information
-    made available during the optimization process in order to vary the accuracy of the objective function computation.
+    This scheme is proposed by Bastin, et al. [1]. The scheme is called a retrospective
+    update scheme as it uses the model function at the current iteration to compute the
+    ratio of the actual reduction and the predicted reduction in the previous trial step,
+    and use this ratio to update the trust region radius. The hypothesis is to exploit the
+    information made available during the optimization process in order to vary the accuracy
+    of the objective function computation.
+
+    [1] Bastin, Fabian, et al. "A retrospective trust-region method for unconstrained
+    optimization." Mathematical programming 123 (2010): 395-418.
     """
     Bastin
 
     """
         RadiusUpdateSchemes.Fan
 
-    This scheme is proposed by [Fan, J.] (https://link.springer.com/article/10.1007/s10589-005-3078-8). It is very much similar to
-    Hei's and Yuan's schemes as it lets the trust region radius depend on the current size (norm) of the objective (merit)
-    function itself. These new update schemes are known to improve local convergence.
+    This scheme is proposed by Fan, J. [1]. It is very much similar to Hei's and Yuan's
+    schemes as it lets the trust region radius depend on the current size (norm) of the
+    objective (merit) function itself. These new update schemes are known to improve local
+    convergence.
+
+    [1] Fan, Jinyan. "Convergence rate of the trust region method for nonlinear equations
+    under local error bound condition." Computational Optimization and Applications 34.2
+    (2006): 215-227.
     """
     Fan
 end