In this paper, some privacy-preserving features for distributed subgradient optimization algorithms are considered. Most of the existing distributed algorithms focus mainly on the algorithm design and convergence analysis, but not the protection of agents' privacy. Privacy is becoming an increasingly important issue in applications involving sensitive information. In this paper, we first show t...

A second-order bundle method to minimize the maximum eigenvalue function François Oustry

We study optimization for collaborative multi-agent planning in factored Markov decision processes (MDPs) with shared resource constraints. Following past research, we derive a distributed planning algorithm for this setting based on Lagrangian relaxation: we optimize a convex dual function which maps a vector of resource prices to a bound on the achievable utility. Since the dual function is n...

This talk surveys applications of space dilation in the perceptron-like algorithms for solving systems of linear inequalities in polynomial time: from the ellipsoid algorithm to the modified perceptron algorithm and the perceptron rescaling algorithm. It also suggests a more general version of the latter algorithm and poses an open problem about the lowest complexity of this approach. Space dil...

The problem of establishing minimum-cost multicast connections in coded networks can be viewed as an optimization problem, and decentralized algorithms were proposed by Lun et al. to compute the optimal subgraph using the subgradient method on the dual problem. However, the convergence rate problem for these algorithms remains open. There are limited results in the literature on the convergence...

Subgradient mappings have many roles in variational analysis, such as the formulation of optimality conditions and, in the special case of normal cone mappings, the statement and analysis of variational inequalities and related expressions. Central to the study of perturbations of solutions to systems of conditions in which subgradient mappings appear are concepts of generalized differentiation...