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We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation (PDE) with unknown parameters (diffusivity and proliferation rate) being spatial fields. We use a dimension-independent globalized, inexact Newton Conjugate Gradient algorithm to solve the PDE-constrained optimization. The required gradient and Hessian actions are also presented using the adjoint method and Lagrangian formalism.