This paper proposes a framework to analyze the concept of power to hydrogen (P2H) for fueling the next generation of aircraft. The impact of introducing new P2H loads is investigated from different aspects namely, cost, carbon emission, and wind curtailment. The newly introduced electric load is calculated based on the idea of replacing the busiest … Read more
The solution of classic discrete-time, finite-horizon linear quadratic regulator (LQR) problem is well known in literature. By casting the solution to be a static state-feedback, we propose a new method that trades off low LQR objective value with closed-loop stability. CitationTo appear on the special issue on the 21st IFAC World Congress 2020, IFAC PapersOnLine.ArticleDownload … Read more
The optimization literature is vast in papers dealing with improvements on the global convergence of augmented Lagrangian schemes. Usually, the results are based on weak constraint qualifications, or, more recently, on sequential optimality conditions obtained via penalization techniques. In this paper we propose a somewhat different approach, in the sense that the algorithm itself is … Read more
Tom Streubel has observed that for functions in abs-normal form, generalized Taylor expansions of arbitrary order $\bd \!- \!1$ can be generated by algorithmic piecewise differentiation. Abs-normal form means that the real or vector valued function is defined by an evaluation procedure that involves the absolute value function $|\cdot|$ apart from arithmetic operations and $\bd$ … Read more
We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and Holderian error bounds and includes logarithmic and entropic error bound found in the exponential cone. It also includes the error bounds obtainable under the theory of … Read more
We consider the problem of maximizing the $\ell_1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well … Read more
Spectral clustering is one of the fundamental unsupervised learning methods widely used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral clustering and it improves the interpretability of the model. This paper considers a widely adopted model for SSC, which can be formulated as an optimization problem over the Stiefel manifold with … Read more
We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve Riemannian optimization problem with only noisy objective function evaluations. Towards this, our main contribution is to propose estimators of the Riemannian gradient and Hessian from noisy objective function evaluations, based on a Riemannian version of the Gaussian … Read more
Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging primal-dual algorithm for minimizing a composite convex function. We also derive a stochastic version of the proposed method which solves empirical risk minimization, and … Read more
Riemannian optimization has drawn a lot of attention due to its wide applications in practice. Riemannian stochastic first-order algorithms have been studied in the literature to solve large-scale machine learning problems over Riemannian manifolds. However, most of the existing Riemannian stochastic algorithms require the objective function to be differentiable, and they do not apply to … Read more