Kona is a Python library targeting partial-differential-equation (PDE) governed optimization problems. To address the high computational cost of such problems, Kona permits parallel execution of linear algebra and optimization operations while remaining agnostic to the implementation details of the underlying PDE solver. To accomplish this, Kona adopts a reverse-communication-inspired interface where the optimization algorithm requests the PDE solver to perform a predetermined set of tasks on solver-generated memory. Consequently, the optimization itself is parallelized as long as the user defines parallel data structures within an abstract vector interface and performs the requested tasks in parallel. This abstraction layer also facilitates the rapid development of new optimization algorithms independently from the underlying PDE solvers. In this paper we describe Kona’s software design in detail, and demonstrate its use on test cases, ranging from analytical verification problems to a PDE-constrained engineering system.