Présidents de session
Chance-constrained programming: Chance constraints in optimal control I
- René Henrion (WIAS Berlin)
Chance-constrained programming: Contributed talks
- Welington de Oliveira (Mines Paris PSL)
Chance-constrained programming: Contributed talks
- Csaba Fabian (John von Neumann University)
Chance-constrained programming: Chance constraints in optimal control II
- René Henrion (WIAS Berlin)
Several problems in practice are described by a set of controlled state equations. If the problem moreover exhibits uncertainty, one can imagine these state equations to be parametrized by a random event or outcome. One may wish to control the final (random) state and ensure that it hits a desired region of space with large enough probability. Motivated by such a setting, we will discuss the...
Optimization problems involving uncertainty in the constraints arise in a wide range of applications. A natural framework for handling such uncertainty is through probability functions. However, these functions are often nonsmooth, which poses challenges for both analysis and computation. In this talk, we propose a regularization approach based on the Moreau envelope applied to a scalarization...
This talk is concerned with a class of risk-neutral stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. This kind of problem appears in the context of optimal control with random differential equation constraints where the state of the system is further constrained almost surely. For this class of problems, we investigate the consistency of...
We study a class of optimal control problems governed by random semilinear parabolic
equations with almost sure state constraints in the space of continuous functions. We
obtain necessary conditions of optimality in the form of a maximum principle with two
multipliers, one for the state constraint and one for the cost function, the multiplier
for the state constraint takes values in a...
We consider the wavelength dimensioning problem in wavelength division multiplexing optical networks, which aims to determine the set of wavelengths assigned to each link to accommodate future connection requests under uncertain traffic conditions. To tackle this, we propose a two-stage chance-constrained mixed-integer programming (2S-CCMIP) model that minimizes the total assigned wavelength...
In this talk, we address joint chance-constrained optimization problems where the only uncertain parameter is the right-hand side coefficients in an inequality system. By leveraging one-dimensional marginals, we construct nonlinear cuts that accurately approximate the probability function, which need not be differentiable or satisfy generalized concavity properties. These cuts are integrated...
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. In this work, we introduce a novel formalism for a prominent problem in stochastic optimization involving complex random variables, which is termed the Complex Chance-Constrained Problem (CCCP). The study specifically...
In this talk, we present a general method for solving the optimal control problem of trajectory planning for autonomous vehicles in continuous time with robustness to uncertainty. In a precedent work [1], we proposed a formulation as a non-linear optimisation problem with an integral cost function including chance constraints. Our present work uses Pontryagin's maximum principle to solve...
Lagrangian relaxation schemes, coupled with a subgradient procedure, are frequently employed to solve chance-constrained optimization models. Subgradient procedures typically rely on step-size update rules. Although there is extensive research on the properties of these step-size update rules, there is little consensus on which rules are most suitable practically; especially, when the...
Gradient computation of multivariate distribution functions calls for a considerable effort. Hence coordinate descent and derivative-free approaches are attractive. This talk deals with constrained convex problems. We perform random descent steps in an approximation scheme that is an inexact cutting-plane method from a dual viewpoint. We prove that the scheme converges and present a...
Chance constraints describe a set of given random inequalities depending on the decision vector satisfied with a large enough probability. They are widely used in decision making under uncertain data in many engineering problems. This talk aims to derive the convexity of chance constraints with elliptically distributed dependent rows via a Gumbel-Hougaard copula. The eventual convexity of...
We consider a two-person zero-sum discounted stochastic game with random rewards and known transition probabilities. The players have opposite objectives and are interested in optimizing the expected discounted reward which they can obtain with a given confidence level when both the players play the worst possible move against each other.
We model such a game problem by defining the...
Time optimal control is a classical problem in control theory.
In the case that the initial state is known exactly, the problem is to find a feasible control that steers the system exactly to the prescribed target state as fast as possible. For systems where the initial state is uncertain, the statement of the problem has to be modified to take into account this uncertainty. We replace the...
The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. It is particularly important for estimating the integration error for certain classes of functions on the sphere. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates when designing optimal sampling schemes for the uniform...
We study optimal control of PDEs under uncertainty with the state variable subject to joint chance constraints. These constraints ensure that the random state variable meets pointwise bounds with high probability. For linear governing PDEs and elliptically distributed random parameters, we prove existence and uniqueness results for almost-everywhere state bounds. We prove variance reduction...
Sweeping processe have been introduced by J.J. Moreau in 1971. These are special differential inclusions where the set-valued right-hand side is represented by the normal cone to some moving set. We consider the optimal control of polyhedral sweeping processe subject to a terminal state constraint. We shall assume that the control is affected by a random perturbation so that the terminal state...
