14,511 research outputs found
Online Primal-Dual Algorithms with Configuration Linear Programs
In this paper, we present primal-dual algorithms for online problems with non-convex objectives. Problems with convex objectives have been extensively studied in recent years where the analyses rely crucially on the convexity and the Fenchel duality. However, problems with non-convex objectives resist against current approaches and non-convexity represents a strong barrier in optimization in general and in the design of online algorithms in particular. In our approach, we consider configuration linear programs with the multilinear extension of the objectives. We follow the multiplicative weight update framework in which a novel point is that the primal update is defined based on the gradient of the multilinear extension. We introduce new notions, namely (local) smoothness, in order to characterize the competitive ratios of our algorithms. The approach leads to competitive algorithms for several problems with convex/non-convex objectives
Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes
Online feedback-based optimization has become a promising framework for
real-time optimization and control of complex engineering systems. This
tutorial paper surveys the recent advances in the field as well as provides
novel convergence results for primal-dual online algorithms with heterogeneous
step sizes for different elements of the gradient. The analysis is performed
for quadratic programs and the approach is illustrated on applications for
adaptive step-size and model-free online algorithms, in the context of optimal
control of modern power systems
Online Assignment Algorithms for Dynamic Bipartite Graphs
This paper analyzes the problem of assigning weights to edges incrementally
in a dynamic complete bipartite graph consisting of producer and consumer
nodes. The objective is to minimize the overall cost while satisfying certain
constraints. The cost and constraints are functions of attributes of the edges,
nodes and online service requests. Novelty of this work is that it models
real-time distributed resource allocation using an approach to solve this
theoretical problem. This paper studies variants of this assignment problem
where the edges, producers and consumers can disappear and reappear or their
attributes can change over time. Primal-Dual algorithms are used for solving
these problems and their competitive ratios are evaluated
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