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Quantum Interior Point Methods (QIPMs) build on classic polynomial time IPMs. With the emergence of quantum computing we apply Quantum Linear System Algorithms (QLSAs) to Newton systems within IPMs to gain quantum speedup in solving Linear Optimization (LO) and Semidefinite Optimization (SDO) problems. Due to their inexact nature, QLSAs mandate the development of inexact variants of IPMs which, due to the inexact computations, by default are inexact infeasible methods.
We propose “quantum inspired” Inexact-Feasible IPMs (IF-IPM) and IF-QIPMs for LO and SDO problems, using novel Newton systems to generate inexact but feasible steps. We show that IF-QIPMs enjoys the to date best iteration complexity. Further, we explore how QLSAs can be used efficiently in iterative refinement schemes to find optimal solutions without excessive calls to QLSAs. The resulting algorithms improve the worst case computational complexity of IPMs.
Modeling disturbances in an ecosystem involves choices along many axes, including whether the disturbances occur continuously in time or at discrete time points. Recently, flow-kick maps have emerged as a framework to study impulsive disturbances that occur periodically in time. For example, instead of representing harvests of a logistic population with the ODE dx/dt = x(1 - x) - h, a flow-kick map composes flow for time t governed x(1 - x) with harvests (kicks) that send x to x - th. Iterating the flow-kick map generates discrete dynamics that capture the interplay between disturbance and recovery processes. To support informed use of flow-kick maps as a modeling tool, we explore their connections to classic ODE disturbance models. We find that continuous disturbance models can be recovered as limits of repeated, discrete ones by taking kicks and flow times to zero while maintaining their proportion. Turning this perspective around, we ask what dynamics we lose, keep, or gain by discretizing disturbance. Under suitable nondegeneracy conditions, fixed points and bifurcations for an ODE model continue to flow-kick models that feature similar disturbance rates and sufficiently small flow times. However, larger flow times can destroy these features or introduce new ones. Flow-kick models thus have the potential to reveal novel insights about disturbance dynamics.
**September 27, 2023**
09:00-09:45 Stijn Vansteelandt (Ghent University)
09:45-10:30 Vanessa Didelez (Leibniz Institute for Prevention Research and Epidemiology - BIPS)
break
11:00-11:45 Peter Bühlmann (ETH Zürich)
11:45-12:30 Dominik Janzing (Amazon Research)
lunch
14:00-14:45 Giusi Moffa (University of Basel)
14:45-15:30 Ricardo Silva (University College London)
**September 28, 2023**
10:00-10:45 Kun Zhang (Carnegie Mellon University)
10:45-11:30 Robin Evans (University of Oxford)
break
11:45-12:30 Niels Richard Hansen (University of Copenhagen)
lunch
14:00-14:45 Niki Kilbertus (Helmholtz / TUM)
14:45-15:30 Mathias Drton (TUM)
See https://collab.dvb.bayern/display/TUMmathstat/Miniworkshop+on+Graphical+Models+and+Causality for more details.