Related papers: Random Field Optimization
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
Designing a fast and efficient optimization method with local optima avoidance capability on a variety of optimization problems is still an open problem for many researchers. In this work, the concept of a new global optimization method…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
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…
Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the…
Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally…
Considerable efforts were made in recent years in devising optimization algorithms for influence maximization in networks. Here we ask: "When do we need optimization?" We use results from statistical mechanics and direct simulations on ER…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
In practice, optimization models are often prone to unavoidable inaccuracies due to dubious assumptions and corrupted data. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on…
The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a…
In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a…
Optimization underpins many of the challenges that science and technology face on a daily basis. Recent years have witnessed a major shift from traditional optimization paradigms grounded on batch algorithms for medium-scale problems to…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…