Related papers: An Abstract Maximum Principle for constrained mini…

We study deterministic nonstationary discrete-time optimal control problems in both finite and infinite horizon. With the aid of Gateaux differentials, we prove a discrete-time maximum principle in analogy with the well-known…

Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…

In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…

The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this…

This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…

A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or…

For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…

In this paper we introduce and study the concept of set extremality for systems of convex sets in vector spaces without topological structures. Characterizations of the extremal systems of sets are obtained in the form of the convex…

Sequential decision making techniques hold great promise to improve the performance of many real-world systems, but computational complexity hampers their principled application. Influence-based abstraction aims to gain leverage by modeling…

As an alternative to the paradigmatic fragmentation problem of a single object crushed into a great number of pieces, we survey a large collection of identical bodies, each one randomly split into two fragments only. While some key features…

The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…

In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative…

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are…