Is it always optimal to choose the same in the optimization problem than the value used

Is it always optimal to choose the same β in the optimization problem than the value used in evaluating the portfolio performance? In other words:

can it be optimal to choose theoretically sub-optimal portfolios based on transaction cost considerations that do not reflect the actual incurred costs? Evaluate the out-of-sample Sharpe ratio after transaction costs for a range of different values of imposed β values.