Related papers: Minimal Convex Environmental Contours
Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we…
Environmental contours are used in structural reliability analysis of marine and coastal structures as an approximate means to locate the boundary of the distribution of environmental variables, and hence sets of environmental conditions…
Environmental contours are an established method in probabilistic engineering design, especially in ocean engineering. The contours help engineers to select the environmental states which are appropriate for structural design calculations.…
We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator.…
Extreme value analysis (EVA) uses data to estimate long-term extreme environmental conditions for variables such as significant wave height and period, for the design of marine structures. Together with models for the short-term evolution…
A set in the Euclidean plane is said to be biconvex if, for some angle $\theta\in[0,\pi/2)$, all its sections along straight lines with inclination angles $\theta$ and $\theta+\pi/2$ are convex sets (i.e, empty sets or segments).…
In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed…
The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…
Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal…
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our…
Minimax lower bounds are pessimistic in nature: for any given estimator, minimax lower bounds yield the existence of a worst-case target vector $\beta^*_{worst}$ for which the prediction error of the given estimator is bounded from below.…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
Convex risk measures play a foundational role in the area of stochastic optimization. However, in contrast to risk neutral models, their applications are still limited due to the lack of efficient solution methods. In particular, the mean…
We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To…
Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such…
We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open sets of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it…
This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do…