相关论文: A PDE-based approach to non-dominated sorting

This paper presents a real-time optimization method for nonlinear model predictive control (NMPC) of systems governed by partial differential equations (PDEs). The NMPC problem to be solved is formulated by discretizing the PDE system in…

We study a growth maximization problem for a continuous time positive linear system with switches. This is motivated by a problem of mathematical biology (modeling growth-fragmentation processes and the PMCA protocol). We show that the…

We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…

For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed…

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…

We consider the homogenization of monotone systems of viscous Hamilton-Jacobi equations with convex nonlinearities set in the stationary, ergodic setting. The primary focus of this paper is on collapsing systems which, as the microscopic…

We propose a new probabilistic numerical scheme for fully nonlinear equation of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem, which is based on the Feynman-Kac representation in [12] by means of control…

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…

In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…

In this paper we propose a new method called ND-Tree-based update (or shortly ND-Tree) for the dynamic non-dominance problem, i.e. the problem of online update of a Pareto archive composed of mutually non-dominated points. It uses a new…

In finite problems comprising objects, situations, and an object- and situation-contingent payoff function, we study the comparative statics of the set of undominated objects, meaning those for which there exists no mixture over objects…

The assortment planning problem is a central piece in the revenue management strategy of any company in the retail industry. In this paper, we study a robust assortment optimization problem for substitutable products under a sequential…

In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…

Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…

Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and…

The paper addresses general constrained and non-linear optimization problems. For some of these notoriously hard problems, there exists a reformulation as an unconstrained, global optimization problem. We illustrate the transformation, and…

A primary challenge in metagenomics is reconstructing individual microbial genomes from the mixture of short fragments created by sequencing. Recent work leverages the sparsity of the assembly graph to find $r$-dominating sets which enable…

Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which…

Devising optimal interventions for diffusive systems often requires the solution of the Hamilton-Jacobi-Bellman (HJB) equation, a nonlinear backward partial differential equation (PDE), that is, in general, nontrivial to solve. Existing…