New Measures for Shaping Trajectories in Dynamic Optimization

TL;DR

This paper introduces a new class of measures inspired by risk measures in stochastic optimization to shape and analyze time-dependent trajectories in dynamic optimization, enhancing control over trajectory features.

Contribution

It proposes a novel framework for applying risk-inspired measures to dynamic optimization, enabling more flexible trajectory shaping and analysis.

Findings

New measures can effectively shape trajectory features.

Implementation demonstrated in Julia's InfiniteOpt.jl package.

Applicable to various trajectory characteristics like costs and quantiles.

Abstract

We propose a new class of measures for shaping time-dependent trajectories in dynamic optimization (DO). The proposed measures are analogous to risk measures used in stochastic optimization (SO) and are inspired by a recently-proposed unifying abstraction for infinite-dimensional optimization. Risk measures are summarizing statistics (e.g., average, variance, quantiles, worst-case values) that are used to shape the probability density of random objectives and constraints. We show that this extensive collection of measures can be applied in DO for computing and manipulating interesting features of time-dependent trajectories (e.g., excursion costs and quantiles). We also discuss how to implement these measures in the Julia modeling package InfiniteOpt.jl.