Related papers: Generalized Scaling for the Constrained Maximum-En…
The best techniques for the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a variety of concave continuous relaxations of the objective function. A standard…
In this paper, we study the maximum entropy sampling problem (MESP) and its variants. MESP seeks to identify a small subset of variables that maximizes the determinant of a covariance submatrix, and is a fundamental model in optimal…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
The generalized maximum-entropy sampling problem (GMESP) is to select an order-$s$ principal submatrix from an order-$n$ covariance matrix, to maximize the product of its $t$ greatest eigenvalues, $0<t\leq s <n$. Introduced more than 25…
The constrained generalized maximum-entropy sampling problem (CGMESP) is to select an order-s principal submatrix from an order-n covariance matrix, subject to some linear side constraints, so as to maximize the product of its t greatest…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-$s$ principle submatrix of a given order $n$ covariance matrix $C$. Exact algorithms are based on a branch-and-bound framework. The…
Based on a factorization of an input covariance matrix, we define a mild generalization of an upper bound of Nikolov (2015) and Li and Xie (2020) for the NP-Hard constrained maximum-entropy sampling problem (CMESP). We demonstrate that this…
The maximum-entropy sampling problem (MESP) aims to select the most informative principal submatrix of a prespecified size from a given covariance matrix. This paper proposes an augmented factorization bound for MESP based on concave…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…
This paper introduces a new global optimization algorithm for solving the generalized linear multiplicative problem (GLMP). The algorithm starts by introducing $\bar{p}$ new variables and applying a logarithmic transformation to convert the…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved…
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…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…