Can Dynare solve general equilibrium (GE) models with non-convex adjustment costs?
Short answer: no.

Dynare, and linearization/perturbation methods in general, are designed for solving


smooth models
approximated around a single point in state space (the steady state).


A model with fixed cost is typically non-smooth, and its behavior away from the steady state may be very different, if e.g. the firm switches from investing to not investing. On the most practical level, a model with fixed cost will typically include equation such as

$$
V = \max \left\{ V^{\text{invest}}, V^{\text{not invest}} \right\},
$$

which cannot be entered into Dynare, because max operator is not supported. On the other hand, first order conditions for convex (e.g. quadratic) adjustment cost are still smooth (one simply adds additional terms to Euler equation for investment) and thus can be easily solved with Dynare.

To actually compute optimal policy with fixed costs, one has typically to use global method, e.g. value function iteration. I'm not aware of any standardized toolbox for solving such problems, so you may need to code your own.

PS: there are some modelling tricks that make the problem smoother, typically in a setting with many, possibly heterogeneous agents/firms. For example, Thomas (2002) keeps track of number of firms depending on how long they didn't invest, and solves the model with standard linearization on this extended state space. Khan &amp; Thomas (2007) assume that the fixed cost is random and iid over time and across firms, so one can average over the realization of fixed cost to obtain smooth value functions. Miao &amp; Wang (2014) use a similar approach in a model with constant returns to scale and show how it aggregates to a version of representative-firm model with only convex adjustment costs.