Optimization-based model calibration is to estimate unknown input variables of a computational model by using optimization techniques. Gradient-based optimization algorithms are often used for efficiency reason. For usage of gradient-based optimization algorithms, if optimization-based model calibration is not formulated as a convex optimization problem, then the optimization may converge into local minima which is not desirable. So far, several calibration metrics, such as likelihood function and probability residual, have been used for an objective function of optimization-based model calibration. However, we have identified that calibrated results using those metrics only is not a convex optimization problem. The response surface of existing calibration metrics shows convex-concave characteristics divided by an inflection line. As long as an inflection line can be obtained, then the optimization can be progressed in a convex area by constraining the calibration variable inside of an inflection line, which means the determinant of Hessian matrix is positive definite or semi positive definite. This paper is to show that optimizationbased model calibration using existing calibration metrics are not convex optimization, thus can result in undesired calibrated result. Then, inflection lines for exiting calibration metrics are derived for assumption on that the system response follows the normal distribution. Lastly, the formulation of a constraint optimization problem using an inflection line is introduced.