update readme with toy example

Author: dance858

README.md

@@ -1,7 +1,7 @@
 # DNLP — Disciplined Nonlinear Programming
 The DNLP package is an extension of [CVXPY](https://www.cvxpy.org/) to general nonlinear programming (NLP).
 DNLP allows smooth functions to be freely mixed with nonsmooth convex and concave functions, 
-with some rules governing how nonsmooth convex and concave functions can appear. For details, see our paper [Disciplined Nonlinear Programming](XXX).
+with some rules governing how the nonsmooth functions can be used. For details, see our paper [Disciplined Nonlinear Programming](XXX).
 
 ---
 ## Installation
@@ -24,10 +24,32 @@ pip install .
 
 ---
 ## Example
-Below we give a toy example. Many more examples, including the ones in the paper, can be found at [DNLP-examples](https://github.com/cvxgrp/dnlp-examples).
+Below we give a toy example where we maximize a convex quadratic function subject to a nonlinear equality constraint.  Many more examples, including the ones in the paper, can be found at [DNLP-examples](https://github.com/cvxgrp/dnlp-examples).
 ```python
 import cvxpy as cp
+import numpy as np 
+import cvxpy as cp
+
+# problem data
+np.random.seed(0)
+n = 3
+A = np.random.randn(n, n)
+A = A.T @ A
+
+# formulate optimization problem
+x = cp.Variable(n)
+obj = cp.Maximize(cp.quad_form(x, A))
+constraints = [cp.sum_squares(x) == 1]
+
+# initialize and solve
+x.value = np.ones(n)
+prob = cp.Problem(obj, constraints)
+prob.solve(nlp=True, verbose=True)
+print("Optimal value from DNLP: ", prob.value)
 
+# the optimal value for this toy problem can also be found by computing the maximum eigenvalue of A
+eigenvalues  = np.linalg.eigvalsh(A)
+print("Maximum eigenvalue:      " , np.max(eigenvalues))
 ```
 
 ---