Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing. This problem is referred to as near-separable NMF and requires that there exists a cone spanned by a small subset of … Read more
Mathematical Programming is Turing complete, and can be used as a general-purpose declarative language. We present a new constructive proof of this fact, and showcase its usefulness by discussing an application to finding the hardest input of any given program running on a Minsky Register Machine. We also discuss an application of Mathematical Programming to … Read more
The alternating direction method of multipliers (ADMM) is now widely used in many fields, and its convergence was proved when two blocks of variables are alternatively updated. It is strongly desirable and practically valuable to extend ADMM directly to the case of a multi-block convex minimization problem where its objective function is the sum of … Read more
This paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semi-definite … Read more
We present a new recovery analysis for a standard compressed sensing algorithm, Iterative Hard Thresholding (IHT) (Blumensath and Davies, 2008), which considers the fixed points of the algorithm. In the context of arbitrary measurement matrices, we derive a sufficient condition for convergence of IHT to a fixed point and a necessary condition for the existence … Read more
We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve state-of-the-art results for various key machine learning optimization problems including SVM, logistic regression, ridge regression, Lasso, and multiclass SVM. … Read more
We are interested in optimizing the co-administration of two drugs for some acute myeloid leukemias (AML), and we are looking for in vitro protocols as a first step. This issue can be formulated as an optimal control problem. The dynamics of leukemic cell populations in culture is given by age-structured partial differential equations, which can … Read more
We consider polynomial differential equations and make a number of contributions to the questions of (i) complexity of deciding stability, (ii) existence of polynomial Lyapunov functions, and (iii) existence of sum of squares (sos) Lyapunov functions. (i) We show that deciding local or global asymptotic stability of cubic vector fields is strongly NP-hard. Simple variations … Read more
Directional sensors are gaining importance due to applications, in- cluding surveillance, detection, and tracking. Such sensors have a limited fi eld-of-view and a discrete set of directions they can be pointed to. The Directional Sensor Control problem (DSCP) consists in assigning a direction of view to each sensor. The location of the targets is known with … Read more
Despite the importance of a thermodynamically stable structure with a conserved fold for protein function, almost all evolutionary models neglect site-site correlations that arise from physical interactions between neighboring amino acid sites. This is mainly due to the difficulty in formulating a computationally tractable model since rate matrices can no longer be used. Here we … Read more