Jean B. Lasserre
LAAS-CNRS, Methods and algorithm in control, Department Member
We consider the class of Markov kernels for which the weak or strong Feller property fails to hold at some discontinuity set. We provide a sim-ple necessary and sufficient condition for existence of an invariant probabi-lity measure as... more
We consider the class of Markov kernels for which the weak or strong Feller property fails to hold at some discontinuity set. We provide a sim-ple necessary and sufficient condition for existence of an invariant probabi-lity measure as well as a Foster-Lyapunov sufficient condition. We also characterize a subclass, the quasi (weak or strong) Feller kernels, for which the sequences of expected occupation measures share the same asymptotic properties as for (weak or strong) Feller kernels. In particular, it is shown that the sequences of expected occupation measures of strong and quasi strong-Feller kernels with an invariant probability measure converge set-wise to an invariant measure.
Research Interests:
In this chapter we study AC-related criteria, some of which have already been studied in previous chapters from a different viewpoint. We begin by introducing some notation and definitions, and then we outline the contents of this chapter.
Research Interests:
As pointed out at the end of the previous chapter, route-based equilibrium models present several drawbacks from the modeling and computational viewpoints. In particular, the independence of route travel times is not well suited when... more
As pointed out at the end of the previous chapter, route-based equilibrium models present several drawbacks from the modeling and computational viewpoints. In particular, the independence of route travel times is not well suited when dealing with overlapping paths.
Research Interests:
Research Interests:
ABSTRACT
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Roughly speaking, given a set of parameters Y and an optimization problem whose description depends on \(y \in Y\) (call it P y), parametric optimization is concerned with the behavior and properties of the optimal value as well as primal... more
Roughly speaking, given a set of parameters Y and an optimization problem whose description depends on \(y \in Y\) (call it P y), parametric optimization is concerned with the behavior and properties of the optimal value as well as primal (and possibly dual) optimal solutions of P y, when y varies in Y. This is a quite challenging problem for which in general only local information around some nominal value y0 of the parameter can be obtained. Sometimes, in the context of optimization with data uncertainty, some probability distribution on the parameter set Y is available and in this context one is also interested in, e.g., the distributions of the optimal value and optimal solutions, all viewed as random variables.
Research Interests:
This paper studies the policy iteration algorithm (PIA) for average cost Markov control processes on Borel spaces. Two classes of MCPs are considered. One of them allows some restricted-growth unbounded cost functions and compact control... more
This paper studies the policy iteration algorithm (PIA) for average cost Markov control processes on Borel spaces. Two classes of MCPs are considered. One of them allows some restricted-growth unbounded cost functions and compact control constraint sets; the other one requires strictly unbounded costs and the control constraint sets may be non-compact. For each of these classes, the PIA yields,
Research Interests:
Considers the vanishing-discount-factor approach to investigate average optimality in Markov control processes with Borel state and action spaces. Under weak assumptions on the discounted differential value function the authors derive... more
Considers the vanishing-discount-factor approach to investigate average optimality in Markov control processes with Borel state and action spaces. Under weak assumptions on the discounted differential value function the authors derive existence of average optimal stationary policies for initial states in a possibly proper subset of the state space. This is in contrast to previous works where an implicit “unichain” assumption ensures optimality for all initial states
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests: Mechanical Engineering, Mathematics, Applied Mathematics, Measure Theory, Computer Science, and 15 moreOptimal Control, Equations of State, Nonlinear Control, Semidefinite Programming, Convexity, Nonlinear system, Lower Bound, Differential equation, Measures, Moments, Electrical And Electronic Engineering, Non Linear Control, Linear Matrix Inequality, Nonlinear Optimal Control, and State Constraints
Research Interests: Mathematics, Applied Mathematics, Computer Science, Multivariate Statistics, Business and Management, and 11 moreSemidefinite Programming, Qa, Gaussian distribution, Exponential distribution, Numerical Analysis and Computational Mathematics, Lower Bound, Upper Bound, Normal Distribution, Semi-definite Programming, Exponential Function, and Order statistic
Research Interests:
Research Interests:
In this chapter we introduce the notions of strong ergodicity and uniform ergodicity of MCs. We study how these notions relate to the concept of “stability” of a transition kernel and to the solvability of the Poisson equation (8.2.1).
Research Interests:
In this paper a hierarchical decomposition-based approach to the planning of an electronic tube production unit is presented. A mid-term planning level computes a manufacturing plan over a discretized horizon by using a decomposition... more
In this paper a hierarchical decomposition-based approach to the planning of an electronic tube production unit is presented. A mid-term planning level computes a manufacturing plan over a discretized horizon by using a decomposition method for solving large linear programming problems. Then a short-term level schedules the first week objective previously calculated. Special attention is paid to the planning level
Research Interests:
Research Interests: Mathematics and Hierarchy
Research Interests:
Research Interests:
Research Interests:
This chapter deals with noncontrolled Markov chains and presents important background material used in later chapters. The reader may omit it and refer to it as needed.
Research Interests:
In this chapter, we study the long-run expected average cost per unit-time criterion, hereafter abbreviated average cost or AC criterion, which is defined as follows.
Research Interests:
Research Interests:
Research Interests:
ABSTRACT
Research Interests:
Research Interests:
In this chapter we briefly review some basic properties of the so-called Harris MCs. As for countable-state MCs, the class of Harris MCs has been extensively studied in the literature, mainly because they are by far the MCs that enjoy the... more
In this chapter we briefly review some basic properties of the so-called Harris MCs. As for countable-state MCs, the class of Harris MCs has been extensively studied in the literature, mainly because they are by far the MCs that enjoy the strongest properties. In fact, we will see that Harris MCs are the exact analogue in uncountable state spaces of the recurrent countable-state MCs.
Research Interests:
... Planning and scheduling in a multi-site environment. ... In this paper, we consider an integrated model for scheduling and planning in a multi-site environment in order to determine a feasible plan, ie a plan with at least a feasible... more
... Planning and scheduling in a multi-site environment. ... In this paper, we consider an integrated model for scheduling and planning in a multi-site environment in order to determine a feasible plan, ie a plan with at least a feasible sequence in each site. ...