Related papers: Box constrained $\ell_1$ optimization in random li…
We examine a constrained Markov decision process under uncertain transition probabilities, with the uncertainty modeled as deviations from observed transition probabilities. We construct the uncertainty set associated with the deviations…
We consider optimization problems constrained by partial differential equations (PDEs) with additional constraints placed on the solution of the PDEs. We develop a general and versatile framework using infinite-valued penalization functions…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
It is well-known that saturated output observations are prevalent in various practical systems and that the $\ell_1$-norm is more robust than the $\ell_2$-norm-based parameter estimation. Unfortunately, adaptive identification based on both…
In this paper we consider solving \emph{noisy} under-determined systems of linear equations with sparse solutions. A noiseless equivalent attracted enormous attention in recent years, above all, due to work of…
The null space condition for $\ell_1$ minimization in compressed sensing is a necessary and sufficient condition on the sensing matrices under which a sparse signal can be uniquely recovered from the observation data via $\ell_1$…
We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
One-dimensional disordered systems with a random potential of a small amplitude and short-range correlations are considered near the initial band edge. The evolution equation is obtained for the mutual ditribution P(\rho,\psi) of the…
This contribution proposes a recursive set-membership method for the ellipsoidal state characterization for discrete-time linear time-varying models with additive unknown disturbances vectors, bounded by possibly degenerate zonotopes and…
This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating $\ell_{0}$ and $\ell_{2,0}$ regularization is minimized over a box constraint. Although such problems arise frequently in…
This paper presents a novel hybrid algorithm for minimizing the sum of a continuously differentiable loss function and a nonsmooth, possibly nonconvex, sparse regularization function. The proposed method alternates between solving a…
Extending well-structured transition systems to incorporate a probabilistic scheduling rule, we define a new class of stochastic well-structured transition systems that includes population protocols, chemical reaction networks, and many…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
We study discrete-time discounted constrained Markov decision processes (CMDPs) on Borel spaces with unbounded reward functions. In our approach the transition probability functions are weakly or set-wise continuous. The reward functions…
Recent studies have explored finite-time dissipation-minimizing protocols for stochastic thermodynamic systems driven arbitrarily far from equilibrium, when granted full external control to drive the system. However, in both simulation and…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
We investigate the optimization of two probabilistic generative models with binary latent variables using a novel variational EM approach. The approach distinguishes itself from previous variational approaches by using latent states as…