2020/06/18 by Irina Subotić, Subotić, Irina, Adrian Hauswirth +3
Engineering · Mathematics · #Advanced Optimization Algorithms Research #Advanced Wireless Network Optimization #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2006.10693
openalex publication_date 2020/06/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Inspired by classical sensitivity results for nonlinear optimization, we\nderive and discuss new quantitative bounds to characterize the solution map and\ndual variables of a parametrized nonlinear program. In particular, we derive\nexplicit expressions for the local and global Lipschitz constants of the\nsolution map of non-convex or convex optimization problems, respectively. Our\nresults are geared towards the study of time-varying optimization problems\nwhich are commonplace in various applications of online optimization, including\npower systems, robotics, signal processing and more. In this context, our\nresults can be used to bound the rate of change of the optimizer. To illustrate\nthe use of our sensitivity bounds we generalize existing arguments to quantify\nthe tracking performance of continuous-time, monotone running algorithms.\nFurther, we introduce a new continuous-time running algorithm for time-varying\nconstrained optimization which we model as a so-called perturbed sweeping\nprocess. For this discontinuous scheme, we establish an explicit bound on the\nasymptotic solution tracking for a class of convex problems.\n