Fix derivative term for odd power rule (#68)

Adjusted the derivative term for the odd power rule to correct edge case where convex relaxations are above the function.

Author: RXGottlieb

.github/workflows/ci.yml

@@ -34,7 +34,7 @@ jobs:
         with:
           version: ${{ matrix.version }}
           arch: ${{ matrix.arch }}
-      - uses: actions/cache@v1
+      - uses: actions/cache@v4
         env:
           cache-name: cache-artifacts
         with:

Project.toml

@@ -1,7 +1,7 @@
 name = "McCormick"
 uuid = "53c679d3-6890-5091-8386-c291e8c8aaa1"
 authors = ["Matthew Wilhelm <[email protected]>"]
-version = "0.13.7"
+version = "0.13.8"
 
 [deps]
 DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"

src/forward_operators/power.jl

@@ -193,7 +193,7 @@ end
     (0.0 <= xL) && (return x^n, n*x^(n - 1))
 
 	root_f(x::Float64, xL::Float64, xU::Float64) = (x^n - xL^n) - (x-xL)*(n)*(x^(n-1));
-	root_df(x::Float64, xL::Float64, xU::Float64) = n*x^(n-1) + xL*n*(n-1)*x - n*x^(n-1) - n*(n-1)*x^(n-1);
+	root_df(x::Float64, xL::Float64, xU::Float64) = (n-1)*n*x^(n-2)*(xL-x);
 	inflection, flag = newton(xU, 0.0, xU, root_f, root_df, xL, xU)
 	flag && (inflection = golden_section(xL, xU, root_f, xL, xU))
 	if x <= inflection
@@ -207,7 +207,7 @@ end
     (0.0 <= xL) && (return dline_seg(^, pow_deriv, x, xL, xU, n))
 
 	root_f(x::Float64, xL::Float64, xU::Float64) = (xU^n-x^n) - (xU-x)*(n)*(x^(n-1));
-	root_df(x::Float64, xL::Float64, xU::Float64) = -n*x^(n-1) - xU*n*(n-1)*x + n*x^(n-1) + n*(n-1)*x^(n-1);
+	root_df(x::Float64, xL::Float64, xU::Float64) = -n^2*xU*x^(n-2) + n^2*x^(n-1) + n*xU*x^(n-2) - n*x^(n-1);
 	inflection, flag = newton(xL, xL, 0.0, root_f, root_df, xL, xU)
 	flag && (inflection = golden_section(xL, xU, root_f, xL, xU))
 	if x <= inflection