diff --git a/Project.toml b/Project.toml
index f26bc20..195b73a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -12,7 +12,7 @@ SolverCore = "ff4d7338-4cf1-434d-91df-b86cb86fb843"
 ADNLPModels = "0.8.13"
 KNITRO = "1.1.0"
 LinearAlgebra = "1.10"
-NLPModels = "0.21.5"
+NLPModels = "0.21.6"
 NLPModelsModifiers = "0.7"
 SolverCore = "0.3"
 Test = "1.10"
diff --git a/docs/src/tutorial.md b/docs/src/tutorial.md
index c427739..2f249d7 100644
--- a/docs/src/tutorial.md
+++ b/docs/src/tutorial.md
@@ -200,3 +200,16 @@ contour!(range(18, 60, step=0.1), range(40_000, 180_000, step=1.0), f, levels=[0
 ```
 
 ![](assets/ex3.png)
+
+## Example: Using L-BFGS (limited-memory) Hessian approximation with KNITRO
+
+You can call KNITRO with the L-BFGS Hessian approximation by passing the following options:
+
+```julia
+stats_knitro = knitro(nlp,
+  hessopt=6,
+  lmsize=10)
+```
+
+This will use the L-BFGS method for Hessian approximation with a history size of 10.
+Note that these options are used by default in `NLPModelsKnitro.jl` if `nlp.meta.hess_available` is `false`.
diff --git a/src/nlp.jl b/src/nlp.jl
index 0d02bd8..ba2c697 100644
--- a/src/nlp.jl
+++ b/src/nlp.jl
@@ -5,6 +5,7 @@ function KnitroSolver(
   linear_api::Bool = true,
   kwargs...,
 )
+  @assert nlp.meta.grad_available && (nlp.meta.ncon == 0 || nlp.meta.jac_available)
   n, m = nlp.meta.nvar, nlp.meta.ncon
 
   kc = KNITRO.KN_new()
@@ -91,7 +92,12 @@ function KnitroSolver(
   else
     jrows, jcols = jac_structure(nlp)
   end
-  hrows, hcols = hess_structure(nlp)
+
+  if nlp.meta.hess_available
+    hrows, hcols = hess_structure(nlp)
+  else
+    hrows, hcols = Int[], Int[]
+  end
 
   # define evaluation callback
   function evalAll(kc, cb, evalRequest, evalResult, userParams)
@@ -175,8 +181,14 @@ function KnitroSolver(
     hessIndexVars2 = convert(Vector{Int32}, hrows .- 1),
   )
 
-  # specify that we are able to provide the Hessian without including the objective
-  KNITRO.KN_set_int_param(kc, KNITRO.KN_PARAM_HESSIAN_NO_F, KNITRO.KN_HESSIAN_NO_F_ALLOW)
+  # Use L-BFGS if the sparse hessian of the Lagrangian is not available
+  if !nlp.meta.hess_available
+    KNITRO.KN_set_int_param_by_name(kc, "hessopt", 6)
+    KNITRO.KN_set_int_param_by_name(kc, "lmsize", 10)
+  else
+    # specify that we are able to provide the Hessian without including the objective
+    KNITRO.KN_set_int_param(kc, KNITRO.KN_PARAM_HESSIAN_NO_F, KNITRO.KN_HESSIAN_NO_F_ALLOW)
+  end
 
   # pass options to KNITRO
   for (k, v) in kwargs