Related papers: A Parametric Approach for Solving Convex Quadratic…
Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance…
This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…
Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
In this paper we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case…
Latent or unobserved phenomena pose a significant difficulty in data analysis as they induce complicated and confounding dependencies among a collection of observed variables. Factor analysis is a prominent multivariate statistical modeling…
This paper addresses the analysis and design of quadratic neural networks, which have been recently introduced in the literature, and their applications to regression, classification, system identification and control of dynamical systems.…
We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
This paper investigates a new class of non-convex optimization, which provides a unified framework for linear precoding in single/multi-user multiple-input multiple-output (MIMO) channels with arbitrary input distributions. The new…
We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method - named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization) - for analyzing high- dimensional data. Unlike in the linear setting where…
We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while respecting the…
Probabilistic model checking aims to prove whether a Markov decision process (MDP) satisfies a temporal logic specification. The underlying methods rely on an often unrealistic assumption that the MDP is precisely known. Consequently,…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…