stochastic control

Barrier Methods Based on Jordan-Hilbert Algebras for Stochastic Optimization in Spin Factors

  • Baha Alzalg
    • Categories Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    We present decomposition logarithmic-barrier interior-point methods based on unital Jordan-Hilbert algebras for infinite-dimensional stochastic second-order cone programming problems in spin factors. The results show that the iteration complexity of the proposed algorithms is independent on the choice of Hilbert spaces from which the underlying spin factors are formed, and so it coincides with the best … Read more

    Optimal Residential Battery Storage Operations Using Robust Data-driven Dynamic Programming

  • Grani A. Hanasusanto
  • Benjamin Leibowicz
  • Nan Zhang
    • Categories Applications - Science and Engineering Tags , , , , ,

    In this paper, we consider the problem of operating a battery storage unit in a home with a rooftop solar photovoltaic (PV) system so as to minimize expected long-run electricity costs under uncertain electricity usage, PV generation, and electricity prices. Solving this dynamic program using standard techniques is computationally burdensome, and is often complicated by … Read more

    On the convergence of the Sakawa-Shindo algorithm in stochastic control

  • Joseph Frédéric Bonnans
  • J. Gianatti
  • Francisco J. Silva
    • Categories Other Topics Tags , ,

    We analyze an algorithm for solving stochastic control problems, based on Pontryagin’s maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of … Read more

    Distributionally robust control of constrained stochastic systems

  • Paul J. Goulart
  • Daniel Kuhn
  • Bart Paul Gerard Van Parys
  • Manfred Morari
    • Categories Control Applications, Robust Optimization Tags , ,

    We investigate the control of constrained stochastic linear systems when faced with only limited information regarding the disturbance process, i.e. when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. The constraints of the first type are required to hold with a given probability for … Read more

    An information-based approximation scheme for stochastic optimization problems in continuous time

  • Daniel Kuhn
    • Categories Infinite Dimensional Optimization, Stochastic Programming Tags , , , ,

    Dynamic stochastic optimization problems with a large (possibly infinite) number of decision stages and high-dimensional state vector are inherently difficult to solve. In fact, scenario tree based algorithms are unsuitable for problems with many stages, while dynamic programming type techniques are unsuitable for problems with many state variables. This article proposes a stage aggregation scheme … Read more