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Differentiable by Design Nonlinear Optimization and its application to Model Predictive Control
Riccardo Zuliani, Efe Balta, John Lygeros
https://arxiv.org/abs/2509.12692 https:…

Differentiable by Design Nonlinear Optimization and its application to Model Predictive Control
Nonlinear optimization-based policies have seen large success in recent years, primarily due to the incredible capabilities of nonlinear Model Predictive Control (nMPC). These policies require solving computationally demanding nonlinear optimization programs (NLP) online at each time-step. The solution map of these NLPs, viewed as a function of the measured state of the system and design parameters, may not be differentiable, which poses significant challenges if the policy is designed with a p…

Replaced article(s) found for cs.SC. https://arxiv.org/list/cs.SC/new
[1/1]:
- Extensions of the Cylindrical Algebraic Covering Method for Quantifiers
Jasper Nalbach, Gereon Kremer

Projective Delineability for Single Cell Construction
Jasper Nalbach, Lucas Michel, Erika \'Abrah\'am, Christopher W. Brown, James H. Davenport, Matthew England, Pierre Mathonet, Na\"im Z\'ena\"idi
https://arxiv.org/abs/2508.00512

Projective Delineability for Single Cell Construction
The cylindrical algebraic decomposition (CAD) is the only complete method used in practice for solving problems like quantifier elimination or SMT solving related to real algebra, despite its doubly exponential complexity. Recent exploration-guided algorithms like NLSAT, NuCAD, and CAlC rely on CAD technology but reduce the computational effort heuristically. Single cell construction is a paradigm that is used in each of these algorithms. The central property on which the CAD algorithm is bas…

A Variant of Non-uniform Cylindrical Algebraic Decomposition for Real Quantifier Elimination
Jasper Nalbach, Erika \'Abrah\'am
https://arxiv.org/abs/2508.00505 https://

A Variant of Non-uniform Cylindrical Algebraic Decomposition for Real Quantifier Elimination
The Cylindrical Algebraic Decomposition (CAD) method is currently the only complete algorithm used in practice for solving real-algebraic problems. To ameliorate its doubly-exponential complexity, different exploration-guided adaptations try to avoid some of the computations. The first such adaptation named NLSAT was followed by Non-uniform CAD (NuCAD) and the Cylindrical Algebraic Covering (CAlC). Both NLSAT and CAlC have been developed and implemented in SMT solvers for satisfiability checkin…