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We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…

Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…

Most exact algorithms for general partially observable Markov decision processes (POMDPs) use a form of dynamic programming in which a piecewise-linear and convex representation of one value function is transformed into another. We examine…

Stochastic proximal point methods have recently garnered renewed attention within the optimization community, primarily due to their desirable theoretical properties. Notably, these methods exhibit a convergence rate that is independent of…

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…

The computation of determinants or their signs is the core procedure in many important geometric algorithms, such as convex hull, volume and point location. As the dimension of the computation space grows, a higher percentage of the total…

Motivated by multi-user optimization problems and non-cooperative Nash games in uncertain regimes, we consider stochastic Cartesian variational inequalities (SCVI) where the set is given as the Cartesian product of a collection of component…

We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and…

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…

We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…

Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…

Many sequential decision problems involve optimizing one objective function while imposing constraints on other objectives. Constrained Partially Observable Markov Decision Processes (C-POMDP) model this case with transition uncertainty and…

Geodesic convexity (g-convexity) is a natural generalization of convexity to Riemannian manifolds. However, g-convexity lacks many desirable properties satisfied by Euclidean convexity. For instance, the natural notions of half-spaces and…

Several attempts to dampen the curse of dimensionnality problem of the Dynamic Programming approach for solving multistage optimization problems have been investigated. One popular way to address this issue is the Stochastic Dual Dynamic…

Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson…

A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…

We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…

Searching for objects amongst clutter is a key ability of visual systems. Speed and accuracy are often crucial: how can the visual system trade off these competing quantities for optimal performance in different tasks? How does the…

A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized…

This paper addresses the problem of optimal control of robotic sensing systems aimed at autonomous information gathering in scenarios such as environmental monitoring, search and rescue, and surveillance and reconnaissance. The information…