Related papers: Subspace selection for projection maximization wit…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
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 consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
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…
The purpose of this paper is to introduce techniques of obtaining optimal ways to determine a d-level quantum state or distinguish such states. It entails designing constrained elementary measurements extracted from maximal abelian subsets…
Algorithm designers typically assume that the input data is correct, and then proceed to find "optimal" or "sub-optimal" solutions using this input data. However this assumption of correct data does not always hold in practice, especially…
Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race.…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…
Given a set of vectors $\F=\{f_1,\dots,f_m\}$ in a Hilbert space $\HH$, and given a family $\CC$ of closed subspaces of $\HH$, the {\it subspace clustering problem} consists in finding a union of subspaces in $\CC$ that best approximates…
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…
Constrained submodular maximization has been extensively studied in the recent years. In this paper, we study adaptive robust optimization with nearly submodular structure (ARONSS). Our objective is to randomly select a subset of items that…
Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the…
Problems of quadratic optimization in Hilbert space often arise when solving ill-posed problems for differential equations. In this case, the target value of the functional is known. In addition, the structure of the functional allows…
Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…
We study the problem of determining the optimal low dimensional projection for maximising the separability of a binary partition of an unlabelled dataset, as measured by spectral graph theory. This is achieved by finding projections which…