arXiv subjects

Lorenz T. Biegler

Publications and source records attributed to Lorenz T. Biegler.

14 recordsLinked to original sources

arXiv2026

Piecewise M-Stationarity and Related Algorithms for Mathematical Programs with Complementarity Constraints

This study explores B-stationarity of mathematical programs with complementarity constraints (MPCCs) and convergence behavior of MPCC algorithms. Special attention is given to the cases with biactive complementarity constraints. First, we propose the concept of piecewise M-stationarity and prove its equivalence to B-stationarity under MPCC-GCQ. Then, we investigate convergence properties of the NCP-based bounding methods we proposed in [31], by requiring MPCC-MFCQ; an interpretation of the algorithm's behavior together with the concept of piecewise M-stationarity leads to a cost reduction in B-stationarity verification. In addition, practical issues related to convergence to non-strongly stationary solutions are discussed, which shows that the NCP-based complementarity reformulations have an advantage in avoiding unbounded multipliers near these solutions.

math.OC↗

arXiv2026

Trust-region filter algorithms utilizing Hessian information for gray-box optimization

Optimizing industrial processes often involves gray-box models that couple algebraic glass-box equations with black-box components lacking analytic derivatives. Such systems challenge derivative-based solvers. The classical trust-region filter (TRF) algorithm provides a robust framework but requires extensive parameter tuning and numerous black-box evaluations. This work introduces four Hessian-informed TRF variants that use projected positive definite Hessians for automatic step scaling and minimal tuning, combined with both low-fidelity (linear, quadratic) and high-fidelity (Taylor series, Gaussian process) surrogates for local black-box approximation. Tested on 25 gray-box benchmarks and five engineering case studies, the new variants achieved up to order-of-magnitude reductions in iterations and black-box evaluations, with reduced sensitivity to tuning parameters relative to the classical TRF algorithm. High-fidelity surrogates solved 92%-100% of problems, compared with 72%-84% for low-fidelity surrogates. The developed TRF methods also outperformed classical derivative-free optimization solvers. Results show that new variants offer robust, scalable alternatives for gray-box optimization.

math.OC↗

arXiv2026

A trust-region funnel algorithm for gray-box optimization

Gray-box optimization, where parts of optimization problems are represented by algebraic models while others are treated as black-box models lacking analytic derivatives, remains a challenge. Trust-region (TR) methods provide a robust framework for gray-box problems through local reduced models (RMs) for black-box components, but they are complex and require extensive parameter tuning. Motivated by recent advances in funnel-based convergence theory for nonlinear optimization, we propose a novel TR funnel algorithm for gray-box optimization, replacing the filter acceptance criterion with a uni-dimensional funnel, maintaining a monotonically decreasing upper bound on approximation error of local black-box RMs. A global convergence proof to a first-order critical point is established. The algorithm, implemented open-source in Pyomo, supports multiple RM forms and globalization strategies (filter or funnel). Benchmark tests show the TR funnel algorithm achieves comparable and often improved performance relative to the classical TR filter method, thus providing a simpler, effective alternative for gray-box optimization.

math.OC↗

arXiv2026

Modeling and Simulation of Nitrogen Generation by Pressure Swing Adsorption for Power-to-Ammonia

Power-to-ammonia (P2A) provides a carbon-free alternative to conventional ammonia production by replacing fossil-based feedstocks with electrolytic hydrogen and nitrogen from air separation. For decentralized P2A systems, pressure swing adsorption (PSA) offers a flexible alternative to cryogenic air separation. However, its industrial implementations are largely proprietary, and open, first-principles models capable of simulating its cyclic, nonlinear transport are scarce in literature. This work presents a first-principles, dynamic, one-dimensional model of a PSA superstructure for nitrogen generation, formulated with thermodynamically consistent equations of state, coupling multicomponent mass, energy, and momentum balances with kinetically limited adsorption on carbon molecular sieves. The resulting system of partial differential-algebraic equations (PDAEs) is semi-discretized using the finite volume method, integrated using diagonally implicit Runge-Kutta methods, and cyclic steady states (CSS) are computed via shooting-based solution methods. The framework is implemented in Julia, combining analytical derivatives with automatic differentiation and utilizing sparse linear algebra for efficient solution of the arising large nonlinear systems. The framework is demonstrated on a two-bed PSA cycle for air separation, comparing spatial and temporal discretization strategies, CSS solution methods, and the effects of ideal versus real-gas thermodynamics on predicted nitrogen purity and recovery. The proposed framework establishes an extensible basis for PSA simulation and optimization.

cs.CE↗

arXiv2026

A Simultaneous Approach for Training Neural Differential-Algebraic Systems of Equations

Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has produced highly influential methods, such as neural ordinary differential equations (NODEs). Recent works extend this line of research to consider neural differential-algebraic systems of equations (DAEs), where some unknown relationships within the DAE are learned from data. Training neural DAEs, similarly to neural ODEs, is computationally expensive, as it requires the solution of a DAE for every parameter update. Further, the rigorous consideration of algebraic constraints is difficult within common deep learning training algorithms such as stochastic gradient descent. In this work, we apply the simultaneous approach to neural DAE problems, resulting in a fully discretized nonlinear optimization problem, which is solved to local optimality and simultaneously obtains the neural network parameters and the solution to the corresponding DAE. We extend recent work demonstrating the simultaneous approach for neural ODEs, by presenting a general framework to solve neural DAEs, with explicit consideration of hybrid models, where some components of the DAE are known, e.g. physics-informed constraints. Furthermore, we present a general strategy for improving the performance and convergence of the nonlinear programming solver, based on solving an auxiliary problem for initialization and approximating Hessian terms. We achieve promising results in terms of accuracy, model generalizability and computational cost, across different problem settings such as sparse data, unobserved states and multiple trajectories. Lastly, we provide several promising future directions to improve the scalability and robustness of our approach.

cs.LG↗

arXiv2025

Asynchronous Distributed Multi-Robot Motion Planning Under Imperfect Communication

This paper addresses the challenge of coordinating multi-robot systems under realistic communication delays using distributed optimization. We focus on consensus ADMM as a scalable framework for generating collision-free, dynamically feasible motion plans in both trajectory optimization and receding-horizon control settings. In practice, however, these algorithms are sensitive to penalty tuning or adaptation schemes (e.g. residual balancing and adaptive parameter heuristics) that do not explicitly consider delays. To address this, we introduce a Delay-Aware ADMM (DA-ADMM) variant that adapts penalty parameters based on real-time delay statistics, allowing agents to down-weight stale information and prioritize recent updates during consensus and dual updates. Through extensive simulations in 2D and 3D environments with double-integrator, Dubins-car, and drone dynamics, we show that DA-ADMM significantly improves robustness, success rate, and solution quality compared to fixed-parameter, residual-balancing, and fixed-constraint baselines. Our results highlight that performance degradation is not solely determined by delay length or frequency, but by the optimizer's ability to contextually reason over delayed information. The proposed DA-ADMM achieves consistently better coordination performance across a wide range of delay conditions, offering a principled and efficient mechanism for resilient multi-robot motion planning under imperfect communication.

cs.RO↗

arXiv2025

An equation-based batch distillation simulation to evaluate the effect of multiplicities in thermodynamic activity coefficients

In this paper, we investigate the influence of multiplicities in activity coefficients on batch distillation processes. In order to do so, we develop a rigorous simulation of batch distillation processes based on the MESH equations. In particular, we propose a novel index reduction method to transform the original index-$2$ system into a well-posed differential-algebraic system of index $1$. With the help of this simulation, we then explore whether the alternative NRTL parameters, which yield indistinguishable activity coefficients and VLE diagrams when compared to the reference data, can produce distinguishable profiles in dynamic simulations. As it turns out, this can happen in general and we explain the reasons behind the dynamic distinguishability.

math.OC↗

arXiv2025

Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees

We propose Conformal Mixed-Integer Constraint Learning (C-MICL), a novel framework that provides probabilistic feasibility guarantees for data-driven constraints in optimization problems. While standard Mixed-Integer Constraint Learning methods often violate the true constraints due to model error or data limitations, our C-MICL approach leverages conformal prediction to ensure feasible solutions are ground-truth feasible. This guarantee holds with probability at least $1{-}α$, under a conditional independence assumption. The proposed framework supports both regression and classification tasks without requiring access to the true constraint function, while avoiding the scalability issues associated with ensemble-based heuristics. Experiments on real-world applications demonstrate that C-MICL consistently achieves target feasibility rates, maintains competitive objective performance, and significantly reduces computational cost compared to existing methods. Our work bridges mathematical optimization and machine learning, offering a principled approach to incorporate uncertainty-aware constraints into decision-making with rigorous statistical guarantees.

cs.LG↗

arXiv2025

On Optimal Control of Hybrid Dynamical Systems using Complementarity Constraints

Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas-liquid tank model and an optimal control problem with a sliding mode solution.

math.OC↗

arXiv2025

Coordinated guidance and control for multiple parafoil system landing

Multiple parafoil landing is an enabling technology for massive supply delivery missions. However, it is still an open question to design a collision-free, computation-efficient guidance and control method for unpowered parafoils. To address this issue, this paper proposes a coordinated guidance and control method for multiple parafoil landing. First, the multiple parafoil landing process is formulated as a trajectory optimization problem. Then, the landing point allocation algorithm is designed to assign the landing point to each parafoil. In order to guarantee flight safety, the collision-free trajectory replanning algorithm is designed. On this basis, the nonlinear model predictive control algorithm is adapted to leverage the nonlinear dynamics model for trajectory tracking. Finally, the parafoil kinematic model is utilized to reduce the computational burden of trajectory calculation, and kinematic model is updated by the moving horizon correction algorithm to improve the trajectory accuracy. Simulation results demonstrate the effectiveness and computational efficiency of the proposed coordinated guidance and control method for the multiple parafoil landing.

cs.RO↗

arXiv2025

Multistage Economic MPC for Systems with a Cyclic Steady State: A Gas Network Case Study

Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. In this paper, we develop a formulation for multistage economic MPC which directly minimizes an economic objective function. The multistage economic MPC framework is extended for systems with a cyclic steady state (CSS) and stability is guaranteed by employing a Lyapunov-based stability constraint. The multistage economic MPC framework is validated on two natural gas network case studies to minimize the net energy consumption during gas transmission. In both instances, the multistage economic MPC effectively manages uncertain demands by preventing constraint violations and guides the network to its optimal cyclic operating conditions. The Lyapunov function remains bounded in both instances, validating the robust stability of the controller.

eess.SY↗

arXiv2024

Conflict-Based Model Predictive Control for Scalable Multi-Robot Motion Planning

This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a similar high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent's kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and reduces the computational cost significantly without compromising the solution quality across a variety of environments. Furthermore, we show that CB-MPC combined with a high-level path planner can effectively substitute computationally expensive full-horizon multi-robot kinodynamic planners.

cs.RO↗

arXiv2019

Contact-Implicit Trajectory Optimization using Orthogonal Collocation

In this paper we propose a method to improve the accuracy of trajectory optimization for dynamic robots with intermittent contact by using orthogonal collocation. Until recently, most trajectory optimization methods for systems with contacts employ mode-scheduling, which requires an a priori knowledge of the contact order and thus cannot produce complex or non-intuitive behaviors. Contact-implicit trajectory optimization methods offer a solution to this by allowing the optimization to make or break contacts as needed, but thus far have suffered from poor accuracy. Here, we combine methods from direct collocation using higher order orthogonal polynomials with contact-implicit optimization to generate trajectories with significantly improved accuracy. The key insight is to increase the order of the polynomial representation while maintaining the assumption that impact occurs over the duration of one finite element.

cs.RO↗

arXiv2018

Surface Wetting Study via Pseudocontinuum Modeling

Accurate estimation of surface wettability for various degrees of hydrophobicity becomes increasingly important in the molecular design of membrane. In this paper, we develop simple yet physically realistic model for estimating contact angle via hybridizing molecular dynamics and pseudocontinuum theory. Molecular dynamics simulations were carried out to compute the macro-scale contact angle between a water droplet and smooth walls from the nanoscale calculations. A macro-level droplet including countless degrees of freedom due to an infinite number of molecules is impossible to be studied directly via atomistic simulations. To resolve this issue, we employed two approaches consisting of the pseudocontinuum approximation and the modified Young-Laplace equation. The former involves the 9-3 Lennard-Jones (L-J) potential and can drastically reduce the degrees of freedom in molecular simulations, while the latter relates the mesoscale contact angle to the realistic one. We altered different parameters including the liquid-surface potential characteristics and the temperature, and calculated the water contact angle by leveraging the mass density profile fitting method to predict the broad spectrum of hydrophobic and hydrophilic substrates. The computational results were compared with the experimental data for various materials including graphite, silicon, and metals. This study suggests that pseudocontinuum modeling is an accurate approach to probe surface wettability for various processes at a low computational cost.

cond-mat.soft↗