Related papers: Fitting Tractable Convex Sets to Support Function …
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our…
Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expressed as the projection of a much simpler set in higher…
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining…
We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…
Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable…
We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank…
Chance-constrained programming is a widely used framework for decision-making under uncertainty, yet its mixed-integer reformulations involve nonconvex mixing sets with a knapsack constraint, leading to weak relaxations and computational…
This paper is motivated by the limit load, limit analysis and shear strength reduction methods, which are commonly employed in geotechnical stability analysis or similar applications. The aim is to make these methods more approachable by…
We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…
The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…
In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from…
Compositional energy-based models can generalize to larger combinatorial reasoning problems by reusing a learned factor energy across many local constraints. In our paper, we show that a key bottleneck in compositional reasoning is not…
The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…
A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…
A number of results related to statistical classification on convex sets are presented. In particular, the focus is on the case where some of the covariates in the data and observation being classified can be missing. The form of the…
Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they…
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…