CVaR-Assisted Custom Penalty Function for Constrained Optimization
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Quantum Physics arXiv:2604.20088 (quant-ph) [Submitted on 22 Apr 2026] Title:CVaR-Assisted Custom Penalty Function for Constrained Optimization Authors:Xin Wei Lee, Hoong Chuin Lau View a PDF of the paper titled CVaR-Assisted Custom Penalty Function for Constrained Optimization, by Xin Wei Lee and 1 other authors View PDF HTML (experimental) Abstract:Constrained combinatorial optimization problems are frequently reformulated as quadratic unconstrained binary optimization (QUBO) models in order to leverage emerging quantum optimization algorithms such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA). However, standard QUBO formulations enforce inequality constraints through slack variables and quadratic penalties, which can significantly increase the problem size and distort the optimization landscape. In this work, we propose a slack-free penalty formulation for constrained binary optimization that eliminates auxiliary slack variables and preserves the feasibility structure of the original problem. The proposed approach introduces a nonlinear custom penalty function to enforce inequality constraints directly in the objective function. To address the computational challenges associated with evaluating nonlinear penalties in variational quantum algorithms, we employ the finite-sampling method that avoids the exponential complexity required by exact expectation computation. Furthermore, we integrate the Conditional Value-at-Risk (CVaR) objective to improve optimization robustness and guide the search toward high-quality solutions. The proposed framework is evaluated on instances of the multi-dimensional knapsack problem, a classical benchmark in combinatorial optimization. We showcase that the proposed custom-penalty formulation combined with CVaR sampling achieves improved optimality gaps and more consistent performance compared with conventional slack-based QUBO formulations. The results suggest that careful penalty design can play a critical role in enabling quantum and hybrid quantum-classical algorithms for constrained optimization problems that arise in operations research. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.20088 [quant-ph] (or arXiv:2604.20088v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.20088 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Xinwei Lee [view email] [v1] Wed, 22 Apr 2026 01:08:38 UTC (90 KB) Full-text links: Access Paper: View a PDF of the paper titled CVaR-Assisted Custom Penalty Function for Constrained Optimization, by Xin Wei Lee and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)