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We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…
We make the case for neural network objects and extend an already existing neural network calculus explained in detail in Chapter 2 on \cite{bigbook}. Our aim will be to show that, yes, indeed, it makes sense to talk about neural network…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares problem arises naturally…
We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…
We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
This paper considers a distributed multi-agent optimization problem, with the global objective consisting of the sum of local objective functions of the agents. The agents solve the optimization problem using local computation and…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
Approximations based on rational functions are widely used in various applications across computational science and engineering. For univariate functions, the adaptive Antoulas-Anderson algorithm (AAA), which uses the barycentric form of a…
The Kolmogorov-Arnold representation is a proven adequate replacement of a continuous multivariate function by an hierarchical structure of multiple functions of one variable. The proven existence of such representation inspired many…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…