Update app.py

app.py

@@ -237,7 +237,7 @@ if st.button("Run MGA Optimization"):
 
 
 st.markdown("""
-    This application uses **Modeling to Generate Alternatives (MGA)** to explore near-optimal solutions in a renewable energy system model. MGA helps to identify alternative configurations that are close to the optimal solution but vary in their specific technological composition, providing flexibility for policy makers and stakeholders who might prioritize factors beyond cost minimization, such as social acceptance or regional preferences[^1].
+    This application uses **Modeling to Generate Alternatives (MGA)** to explore near-optimal solutions in a renewable energy system model. MGA helps to identify alternative configurations that are close to the optimal solution but vary in their specific technological composition, providing flexibility for policy makers and stakeholders who might prioritize factors beyond cost minimization, such as social acceptance or regional preferences [1].
     """)
 
 st.write("## Objective Function and Cost Minimization")
@@ -275,10 +275,10 @@ st.latex(r"""
 """)
 st.markdown("""
 where:
-- $\epsilon$ is the cost deviation percentage (e.g., if $\epsilon = 0.05$), then the solution can be up to 5% more expensive than the optimal cost),
+- $\epsilon$ is the cost deviation percentage (e.g. if $\epsilon = 0.05$), then the solution can be up to 5% more expensive than the optimal cost),
 - ${Optimal\, Cost}$ is the minimum cost obtained from the initial optimization.
 
-This constraint allows for flexibility in cost, enabling the exploration of solutions that are **near-optimal** but differ in terms of installed capacities for each technology[^2].
+This constraint allows for flexibility in cost, enabling the exploration of solutions that are **near-optimal** but differ in terms of installed capacities for each technology [2].
 """)
 
 st.markdown("""
@@ -316,7 +316,7 @@ Through MGA, we can make more **informed decisions** about the renewable energy
 """)
 
 st.markdown("""
-[^1]: E. D. Brill, “The Use of Optimization Models in Public-Sector Planning,” Management Science, vol. 25, no. 5, pp. 413–422, 1979, Publisher: INFORMS, ISSN:
+[1] E. D. Brill, “The Use of Optimization Models in Public-Sector Planning,” Management Science, vol. 25, no. 5, pp. 413–422, 1979, Publisher: INFORMS, ISSN:
 0025-1909. DOI: 10.1287/mnsc.25.5.413.
-[^2]: Neumann, Fabian, and Tom Brown. "The near-optimal feasible space of a renewable power system model." Electric Power Systems Research, vol. 190, 2021, p. 106690. https://doi.org/10.1016/j.epsr.2020.106690.
+[2] Neumann, Fabian, and Tom Brown. "The near-optimal feasible space of a renewable power system model." Electric Power Systems Research, vol. 190, 2021, p. 106690. https://doi.org/10.1016/j.epsr.2020.106690.
 """)