Minimisation at a specific point

def objective_function(params):
    interp_func = interp1d(STK, params, kind='cubic', fill_value='extrapolate')
    interpolated_ivs = interp_func(STK)
    return np.sum((interpolated_ivs - IV) ** 2)

def constraint(params):
    interp_func = interp1d(STK, params, kind='cubic', fill_value='extrapolate')
    atm_IV = interp_func(CMP)
    min_IV = min(interp_func(np.arange(min(STK), max(STK) + 0.0001, 0.0001)))
    return atm_IV - min_IV

initial_params = IV

constraints = {'type': 'ineq', 'fun': constraint}

result = minimize(objective_function, initial_params, constraints=constraints)

if result.success:
    optimized_params = result.x
    adj_interp_func = interp1d(STK, optimized_params, kind='cubic', fill_value='extrapolate')

    interpolated_strikes = np.round(np.arange(min(STK), max(STK) + 0.0001, 0.0001),4)
    interpolated_ivs = np.round(adj_interp_func(interpolated_strikes),4)

    for i in range(len(interpolated_strikes)):
        delta_call = black_scholes_delta(CMP, interpolated_strikes[i], DTE_N, r, sigma, 'C')
        delta_put = black_scholes_delta(CMP, interpolated_strikes[i], DTE_N, r, sigma, 'P')
        call_deltas.append(delta_call)
        put_deltas.append(delta_put)

    del_25_c_strike = interpolated_strikes[np.argmin(np.abs(np.array(call_deltas)-0.25))]
    del_25_p_strike = interpolated_strikes[np.argmin(np.abs(np.array(put_deltas)+0.25))]

    strikes_reqd = [CMP, del_25_c_strike, del_25_p_strike]
    IV_reqd = []
    for i in strikes_reqd:
        IV_reqd.append(interpolated_ivs[np.argmin(np.abs(interpolated_strikes-i))])
else:
    print("Optimization failed:", result.message)

print(f"Strikes - ATM, 25_Delta_Call, 25_Delta_Put are: {strikes_reqd}")
print(f"IVs - ATM, 25_Delta_Call, 25_Delta_Put are: {IV_reqd}")

# Plot the original data and the interpolated curve
plt.figure(figsize=(8, 4))
plt.plot(interpolated_strikes, interpolated_ivs, label='Adjusted Interpolated Curve')
plt.scatter(STK, IV_N, color='red', label='Market Data')
plt.title('Interpolated IV_F1 vs. F1')
plt.xlabel('F1')
plt.ylabel('IV_F1')
plt.legend()
plt.grid(True)
plt.show()