You need to liquidate 1 million shares of an illiquid stock today. Suppose the temporary market impact is proportional to the square root of your trading rate. You write an objective function penalizing execution cost and inventory risk, but your optimizer outputs a weird, discontinuous trading trajectory. What fundamental mathematical issue does a square root impact introduce to your optimization, and how do you solve it in practice?

你需要今天之内平仓100万股某流动性差的股票。假设临时市场冲击（temporary impact）与你的交易速率成平方根关系。你写了一个包含冲击成本和风险惩罚的目标函数，但优化器给出了奇怪的不连续交易曲线。平方根冲击会对最优化造成什么根本性的数学问题？实操中你怎么解决？