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The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
In concurrency theory, weak bisimilarity is often used to relate processes exhibiting the same observable behaviour. The probabilistic environment gives rise to several generalisations; we study the infinitary semantics, which abstracts…
We investigate the existence of bounded-memory consistent estimators of various statistical functionals. This question is resolved in the negative in a rather strong sense. We propose various bounded-memory approximations, using techniques…
Parameterized max-affine (PMA) and parameterized log-sum-exp (PLSE) networks are proposed for general decision-making problems. The proposed approximators generalize existing convex approximators, namely, max-affine (MA) and log-sum-exp…
Structured prediction can be considered as a generalization of many standard supervised learning tasks, and is usually thought as a simultaneous prediction of multiple labels. One standard approach is to maximize a score function on the…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
We formalize the observation that the same summability methods converge in a Banach space $X$ and its dual $X^*$. At the same time we determine conditions under which these methods converge in the weak and weak*-topologies on $X$ and $X^*$…
Simulation Optimization (SO) refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation---discrete or…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees,…
In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
The paper studies a general norm minimization problem on a product of normed vector spaces. We establish dual necessary and sufficient optimality conditions and derive explicit formulas for the corresponding solution sets. These formulas…
We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the…
Data with multiple functional recordings at each observational unit are increasingly common in various fields including medical imaging and environmental sciences. To conduct inference for such observations, we develop a paired two-sample…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
This paper explores the fundamental properties of distributed minimization of a sum of functions with each function only known to one node, and a pre-specified level of node knowledge and computational capacity. We define the optimization…
Min-max optimization problems, also known as saddle point problems, have attracted significant attention due to their applications in various fields, such as fair beamforming, generative adversarial networks (GANs), and adversarial…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
In the present work we consider rational best approximations to the exponential function that minimize a uniform error on a subset of the imaginary axis. Namely, Chebyshev approximation and unitary best approximation where the latter is…