In classic mathematical finance, a trader's actions have no direct influence on the asset price. For small trades this is a reasonable assumption, but large trades fire back at the underlying price. We consider a transient linear price impact model in discrete time, and find a deterministic and unique optimal trading strategy when the decay of price impact is given as a positive-definite quadratic form. Examples of the associated so-called resilience functions show a new type of price manipulation, which will be called transaction-triggered price manipulation. To exclude this kind of price manipulation, convexity of the resilience function appears to be both necessary and sufficient. Since nonconstant, convex functions generate positive definite quadratic forms, standard price manipulation is excluded in this case as well. The effects of risk aversion can be handled similarly to the way the standard optimal order execution problem is solved. The discrete-time model can be extended to continuous time, and we find some similar results. It appears that optimal strategies can be characterized as measure-valued solutions of a generalized Fredholm integral equation of the first kind. However, to guarantee the existence of an optimal trading strategy, positive definiteness does not hold, and we need convexity of the decay kernel. As in the discrete-time case, this excludes the existence of transaction-triggered price manipulation strategies.