  We propose an energy-optimized invariant energy quadratization method to
solve the gradient flow models in this paper, which requires only one linear
energy-optimized step to correct the auxiliary variables on each time step. In
addition to inheriting the benefits of the baseline and relaxed invariant
energy quadratization method, our approach has several other advantages.
Firstly, in the process of correcting auxiliary variables, we can directly
solve linear programming problem by the energy-optimized technique, which
greatly simplifies the nonlinear optimization problem in the previous relaxed
invariant energy quadratization method. Secondly, we construct new linear
unconditionally energy stable schemes by applying backward Euler formulas and
Crank-Nicolson formula, so that the accuracy in time can reach the first- and
second-order. Thirdly, comparing with relaxation technique, the modified energy
obtained by energy-optimized technique is closer to the original energy,
meanwhile the accuracy and consistency of the numerical solutions can be
improved. Ample numerical examples have been presented to demonstrate the
accuracy, efficiency and energy stability of the proposed schemes.
