We perform research and development of advanced algorithms for engineering-based optimization. This includes engineering design optimization, model calibration (i.e., parameter estimation), and material identification (or inversion). Often, the problems we address have equality constraints given by solutions to partial differential equations. We implement these algorithms in our flagship software tools DAKOTA (http://dakota.sandia.gov) and Trilinos (https://trilinos.github.io/). Our optimization capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty.