Fix spelling errors and add typos configuration

.typos.toml

@@ -1,11 +1,79 @@
 [default.extend-words]
-AGS = "AGS"
-# Additional SciML terms
+# Julia-specific functions  
+indexin = "indexin"
+findfirst = "findfirst"
+findlast = "findlast"
+eachindex = "eachindex"
 setp = "setp"
 getp = "getp"
-indexin = "indexin"
+setu = "setu"
+getu = "getu"
+
+# Mathematical/scientific terms
+jacobian = "jacobian"
+hessian = "hessian" 
+eigenvalue = "eigenvalue"
+eigenvector = "eigenvector"
+discretization = "discretization"
+linearization = "linearization"
+parameterized = "parameterized"
+discretized = "discretized"
+vectorized = "vectorized"
+
+# Common variable patterns in Julia/SciML
 ists = "ists"
 ispcs = "ispcs"
+osys = "osys"
+rsys = "rsys"
+usys = "usys"
+fsys = "fsys"
 eqs = "eqs"
 rhs = "rhs"
-MTK = "MTK"
+lhs = "lhs"
+ode = "ode"
+pde = "pde"
+sde = "sde"
+dde = "dde"
+bvp = "bvp"
+ivp = "ivp"
+
+# Common abbreviations
+tol = "tol"
+rtol = "rtol"
+atol = "atol"
+idx = "idx"
+jdx = "jdx"
+prev = "prev"
+curr = "curr"
+init = "init"
+tmp = "tmp"
+vec = "vec"
+arr = "arr"
+dt = "dt"
+du = "du"
+dx = "dx"
+dy = "dy"
+dz = "dz"
+
+# Algorithm/type suffixes
+alg = "alg"
+prob = "prob"
+sol = "sol"
+cb = "cb"
+opts = "opts"
+args = "args"
+kwargs = "kwargs"
+
+# Scientific abbreviations
+ND = "ND"
+nd = "nd"
+MTK = "MTK"
+ODE = "ODE"
+PDE = "PDE"
+SDE = "SDE"
+
+# Optimization specific terms
+TikTak = "TikTak"  # Legitimate algorithm name in MultistartOptimization
+Tak = "Tak"  # Part of TikTak algorithm name
+opf = "opf"  # Optimal Power Flow abbreviation
+AGS = "AGS"  # Legitimate NLopt algorithm name

lib/OptimizationNLPModels/src/OptimizationNLPModels.jl

@@ -7,7 +7,7 @@ using Reexport
     OptimizationFunction(nlpmodel::AbstractNLPModel, adtype::AbstractADType = NoAD())
 
 Returns an `OptimizationFunction` from the `NLPModel` defined in `nlpmodel` where the
-available derivates are re-used from the model, and the rest are populated with the
+available derivatives are re-used from the model, and the rest are populated with the
 Automatic Differentiation backend specified by `adtype`.
 """
 function SciMLBase.OptimizationFunction(nlpmodel::AbstractNLPModel,