A one dimensional deterministic free boundary problem.
A pension fund in the accumulation phase: a stochastic control approach
In this paper we propose and study a continuous time stochastic model of optimal allocation for a defined contribution pension fund in the accumulation phase. The level of wealth is constrained to stay above a "solvency level". The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. The model is naturally formulated as an optimal stochastic control problem with state constraints and is treated by the dynamic programming approach. We show...
A Solution of the 'Converse Canonical Problem' for Multiple Integrals in the Calculus of Variations (Short Communication)
A Solution of the 'Converse Canonical Problem' for Multiple Integrals in the Calculus of Variations
A study in the Lagranges variational problem considered in the large.
A synthesis of time-optimal controls in the presence of saturated singular arcs.
A timed Petri net framework to find optimal IRIS schedules
A viscosity solution method for Shape-From-Shading without image boundary data
In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884],...
Abnormality of trajectory in sub-Riemannian structure
In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, -rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not -rigid and which can be minimizing...
About secretary problems
Adaptive control for sequential design
The optimal experiment for estimating the parameters of a nonlinear regression model usually depends on the value of these parameters, hence the problem of designing experiments that are robust with respect to parameter uncertainty. Sequential designpermits to adapt the experiment to the value of the parameters, and can thus be considered as a robust design procedure. By designing theexperiments sequentially, one introduces a feedback of information, and thus dynamics, into the design procedure....
Adaptive resource allocation to stochastic multimodal projects: a distributed platform implementation in Java
Adjoint methods for obstacle problems and weakly coupled systems of PDE
The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.
Almost continuous solutions of geometric Hamilton–Jacobi equations
Almost sure properties of controlled diffusions and worst case properties of deterministic systems
We compare a general controlled diffusion process with a deterministic system where a second controller drives the disturbance against the first controller. We show that the two models are equivalent with respect to two properties: the viability (or controlled invariance, or weak invariance) of closed smooth sets, and the existence of a smooth control Lyapunov function ensuring the stabilizability of the system at an equilibrium.
An algorithm for construction of ε-value functions for the Bolza control problem
The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper...
An application of dynamic programming principle in corporate international optimal investment and consumption choice problem.
An approach of deterministic control problems with unbounded data
An approximation scheme for the optimal control of diffusion processes
An autonomous vehicle sequencing problem at intersections: A genetic algorithm approach
This paper addresses a vehicle sequencing problem for adjacent intersections under the framework of Autonomous Intersection Management (AIM). In the context of AIM, autonomous vehicles are considered to be independent individuals and the traffic control aims at deciding on an efficient vehicle passing sequence. Since there are considerable vehicle passing combinations, how to find an efficient vehicle passing sequence in a short time becomes a big challenge, especially for more than one intersection....