I came across this optimization problem but I did not learn optimization theory previously. Could anyone provide some thoughts on how to solve them?
$ \begin{align} \text{minimize} & \quad e^{-\frac{{t_1}^2}{2}} + e^{-\frac{{t_2}^2}{2}} + e^{-\frac{{t_3}^2}{2}} - e^{-\frac{(t_1+t_2)^2}{2}} - e^{-\frac{(t_2+t_3)^2}{2}} + e^{-\frac{(t_1+t_2 + t_3)^2}{2}}\\ \text{subject to} & \quad t_1 + t_2 + t_3 \leq K, \\ & \quad t_1, t_2, t_3 \geq 0 \end{align} $