We extend coordinate descent to manifold domains, and provide convergence analyses for geodesically convex and non-convex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and tangent subspaces of a manifold. Hence, our method is called tangent subspace descent (TSD). The core principle behind ensuring convergence of … Read more
We consider quadratic optimization in variables (x,y), 0
We study structured multi-armed bandits, which is the problem of online decision-making under uncertainty in the presence of structural information. In this problem, the decision-maker needs to discover the best course of action despite observing only uncertain rewards over time. The decision- maker is aware of certain structural information regarding the reward distributions and would … Read more
In this paper, we develop a Monte-Carlo based heuristic approach to approximate the objective function in long horizon optimal control problems. In this approach, we evolve the system state over multiple trajectories into the future while sampling the noise disturbances at each time-step, and find the weighted average of the costs along all the trajectories. … Read more
This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers, and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition … Read more
We introduce a new class of two-stage stochastic uncapacitated facility location problems under system nervousness considerations. The location and allocation decisions are made under uncertainty, while the allocation decisions may be altered in response to the realizations of the uncertain parameters. A practical concern is that the uncertainty-adaptive second-stage allocation decisions might substantially deviate from … Read more
In \cite{siebert2019linear} the authors present a set of integer programs (IPs) for the Steiner tree problem, which can be used for both, the directed and the undirected setting of the problem. Each IP finds an optimal Steiner tree with a specific structure. A solution with the lowest cost, corresponds to an optimal solution to the … Read more
While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD) constraint and only enforce PSD-ness on smaller k times k principal submatrices — we call this the sparse SDP relaxation. Surprisingly, … Read more
Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial that surveys … Read more
We consider a generic class of chance-constrained optimization problems with heavy-tailed (i.e., power-law type) risk factors. In this setting, we use the scenario approach to obtain a constant approximation to the optimal solution with a computational complexity that is uniform in the risk tolerance parameter. We additionally illustrate the efficiency of our algorithm in the … Read more