In this work, a new nonlinear framework is presented for superior reconstructions in ultrasound-modulated optical tomography. The framework is based on minimizing a functional comprising of least squares data fitting term along with additional sparsity priors that promote high contrast, subject to the photon-propagation diffusion equation. The resulting optimization problem is solved using a sequential quadratic Hamiltonian scheme, based on the Pontryagin’s maximum principle, that does not involve semi-smooth calculus and is easy to implement.