Submodularity in Binary Optimal Control of PDEs
نویسندگان
چکیده
We show that in a large class of semilinear elliptic binary optimal control problems, the point-wise states are submodular functions in the control variables almost everywhere. Moreover, we discuss how to use this result in order to design global optimization algorithms for such problems. To our knowledge, this is the rst time submodularity is investigated in the context of optimal control.
منابع مشابه
Evaluating the true potential of diffusion-based inpainting in a compression context
Partial differential equations (PDEs) are able to reconstruct images accurately from a small fraction of their image points. These inpainting capabilities allow compression codecs with sophisticated anisotropic PDEs to compete with transform-based methods like JPEG 2000. For simple linear PDEs, optimal known data can be found with powerful optimisation strategies. However, the potential of thes...
متن کاملSubmodularity of Storage Placement Optimization in Power Networks
In this paper, we consider the problem of placing energy storage resources in a power network when all storage devices are optimally controlled to minimize system-wide costs. We propose a discrete optimization framework to accurately model heterogeneous storage capital and installation costs as these fixed costs account for the largest cost component in most grid-scale storage projects. Identif...
متن کاملOrdinal notions of submodularity
We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to David Kreps (A Representation Theorem for “Preference for Flexibility”, Econometrica, 1979) and one is a weakening of a notion due to Paul Milgrom and Chris Shannon (Monotone Comparative Statics, Econometrica, 1994). We show that any ref...
متن کاملOptimal Boundary Control & Estimation of Diffusion-Reaction PDEs
This paper considers the optimal control and optimal estimation problems for a class of linear parabolic diffusion-reaction partial differential equations (PDEs) with actuators and sensors at the boundaries. Diffusion-reaction PDEs with boundary actuation and sensing arise in a multitude of relevant physical systems (e.g. magneto-hydrodynamic flows, chemical reactors, and electrochemical conver...
متن کاملSubmodularity in Conic Quadratic Mixed 0-1 Optimization
We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint ove...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016