Related papers: Linear embedding of free energy minimization
This paper presents a convex optimization framework for eco-driving and vehicle energy management problems. We will first show that several types of eco-driving and vehicle energy management problems can be modelled using the same notions…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
This paper is concerned with a priori error estimates for the local incremental minimization scheme, which is an implicit time discretization method for the approximation of rate-independent systems with non-convex energies. We first show…
In stochastic convex optimization the goal is to minimize a convex function $F(x) \doteq {\mathbf E}_{{\mathbf f}\sim D}[{\mathbf f}(x)]$ over a convex set $\cal K \subset {\mathbb R}^d$ where $D$ is some unknown distribution and each…
Linearized models of power systems are often desirable to formulate tractable control and optimization problems that still reflect real-world physics adequately under various operating conditions. In this paper, we propose an approach that…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We present a novel class of minimax optimal control problems with positive dynamics, linear objective function and homogeneous constraints. The proposed problem class can be analyzed with dynamic programming and an explicit solution to the…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
We consider a nonlinear convex stochastic homogenization problem, in a stationary setting. In practice, the deterministic homogenized energy density can only be approximated by a random apparent energy density, obtained by solving the…
In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…
In this paper, I investigate more closely the recently proposed Free Energy Monte Carlo algorithm that is devised in particular for calculations where conventional Monte Carlo simulations struggle with ergodicity problems. The simplest…