Related papers: Infinite dimensional optimistic optimisation with …
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
We investigate the calibration of estimations to increase performance with an optimal monotone transform on the estimator outputs. We start by studying the traditional square error setting with its weighted variant and show that the optimal…
We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…
We study the limit computability of finding a global optimum of a continuous function. We give a short proof to show that the problem of checking whether a point is a global minimum is not limit computable. Thereby showing the same for the…
We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and continuous time. The set of all invariant measures is characterized as the feasible…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. The…
Maximization of submodular functions under various constraints is a fundamental problem that has been studied extensively. A powerful technique that has emerged and has been shown to be extremely effective for such problems is the…
The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…
We consider problems in which a mobile robot samples an unknown function defined over its operating space, so as to find a global optimum of this function. The path traveled by the robot matters, since it influences energy and time…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
It is strange but fruitful to think about the functions as random processes. Any function can be viewed as a martingale (in many different ways) with discrete time. But it can be useful to have continuous time too. Processes can emulate…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces…