EIQP: Execution-time-certified and Infeasibility-detecting QP Solver
Liang Wu, Wei Xiao, Richard D. Braatz

TL;DR
This paper introduces EIQP, a novel infeasible interior-point method for convex quadratic programming that certifies solution feasibility or detects infeasibility within a guaranteed time, suitable for real-time control applications.
Contribution
It proposes a new infeasible IPM with exact, data-independent iteration complexity for real-time convex QP solving, including infeasibility detection, with accessible implementation.
Findings
Achieves $O(rac{ ext{log}(rac{n+1}{ ext{epsilon}})}{- ext{log}(1-rac{0.414213}{ ext{sqrt}(n+1)})})$ iteration complexity
Provides a simple, line-search-free implementation with MATLAB, Julia, and Python interfaces
Demonstrates effectiveness in real-time control scenarios
Abstract
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can either return a solution within a predefined level of optimality or detect QP infeasibility before the predefined sampling time is a pressing requirement. This article considers convex QP (including linear programming) and adopts its homogeneous formulation to achieve infeasibility detection. Exploiting this homogeneous formulation, this article proposes a novel infeasible interior-point method (IPM) algorithm with the best theoretical iteration complexity that feasible IPM algorithms enjoy. The iteration complexity is proved to be \textit{exact} (rather than an upper bound), \textit{simple to calculate}, and \textit{data independent},…
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Taxonomy
TopicsCloud Computing and Resource Management · Parallel Computing and Optimization Techniques · Fault Detection and Control Systems
