9,884 research outputs found
Exploiting Chordality in Optimization Algorithms for Model Predictive Control
In this chapter we show that chordal structure can be used to devise
efficient optimization methods for many common model predictive control
problems. The chordal structure is used both for computing search directions
efficiently as well as for distributing all the other computations in an
interior-point method for solving the problem. The chordal structure can stem
both from the sequential nature of the problem as well as from distributed
formulations of the problem related to scenario trees or other formulations.
The framework enables efficient parallel computations.Comment: arXiv admin note: text overlap with arXiv:1502.0638
OSQP: An Operator Splitting Solver for Quadratic Programs
We present a general-purpose solver for convex quadratic programs based on
the alternating direction method of multipliers, employing a novel operator
splitting technique that requires the solution of a quasi-definite linear
system with the same coefficient matrix at almost every iteration. Our
algorithm is very robust, placing no requirements on the problem data such as
positive definiteness of the objective function or linear independence of the
constraint functions. It can be configured to be division-free once an initial
matrix factorization is carried out, making it suitable for real-time
applications in embedded systems. In addition, our technique is the first
operator splitting method for quadratic programs able to reliably detect primal
and dual infeasible problems from the algorithm iterates. The method also
supports factorization caching and warm starting, making it particularly
efficient when solving parametrized problems arising in finance, control, and
machine learning. Our open-source C implementation OSQP has a small footprint,
is library-free, and has been extensively tested on many problem instances from
a wide variety of application areas. It is typically ten times faster than
competing interior-point methods, and sometimes much more when factorization
caching or warm start is used. OSQP has already shown a large impact with tens
of thousands of users both in academia and in large corporations
Equilibrium points for Optimal Investment with Vintage Capital
The paper concerns the study of equilibrium points, namely the stationary
solutions to the closed loop equation, of an infinite dimensional and infinite
horizon boundary control problem for linear partial differential equations.
Sufficient conditions for existence of equilibrium points in the general case
are given and later applied to the economic problem of optimal investment with
vintage capital. Explicit computation of equilibria for the economic problem in
some relevant examples is also provided. Indeed the challenging issue here is
showing that a theoretical machinery, such as optimal control in infinite
dimension, may be effectively used to compute solutions explicitly and easily,
and that the same computation may be straightforwardly repeated in examples
yielding the same abstract structure. No stability result is instead provided:
the work here contained has to be considered as a first step in the direction
of studying the behavior of optimal controls and trajectories in the long run
Maximum Principle for Linear-Convex Boundary Control Problems applied to Optimal Investment with Vintage Capital
The paper concerns the study of the Pontryagin Maximum Principle for an
infinite dimensional and infinite horizon boundary control problem for linear
partial differential equations. The optimal control model has already been
studied both in finite and infinite horizon with Dynamic Programming methods in
a series of papers by the same author, or by Faggian and Gozzi. Necessary and
sufficient optimality conditions for open loop controls are established.
Moreover the co-state variable is shown to coincide with the spatial gradient
of the value function evaluated along the trajectory of the system, creating a
parallel between Maximum Principle and Dynamic Programming. The abstract model
applies, as recalled in one of the first sections, to optimal investment with
vintage capital
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