Related papers: Solving equations and optimization problems with u…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
We study the problem of \emph{robust satisfiability} of systems of nonlinear equations, namely, whether for a given continuous function $f:\,K\to\mathbb{R}^n$ on a~finite simplicial complex $K$ and $\alpha>0$, it holds that each function…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods. This basic operation typically consists in solving an intermediary (hopefully simpler) optimization…
Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…
Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have…
Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we…
Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
This work advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the…
We propose a refinement of the maxmin approach to robustness. A mechanism's payoff guarantee over an ambiguity set is \emph{robust} if the guarantee is approximately satisfied at priors near the ambiguity set (in the weak topology). We show…
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…