# A Penalty-Based Guardrail Algorithm for Non-Decreasing Optimization with Inequality Constraints

arXiv: https://arxiv.org/abs/2405.01984 · HTML: https://mlsanity.com/paper/2405.01984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 55 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimization](https://mlsanity.com/paper/1908.02734/) (2019)
- [An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints](https://mlsanity.com/paper/1906.11357/) (2019)
- [Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints](https://mlsanity.com/paper/1908.01871/) (2019)
- [Iteration complexity of inexact augmented Lagrangian methods for constrained convex programming](https://mlsanity.com/paper/1711.05812/) (2017)
- [Input Convex Neural Networks for Building MPC](https://mlsanity.com/paper/2011.13227/) (2020)
- [Complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programs](https://mlsanity.com/paper/1802.03504/) (2018)
- [Enabling Research through the SCIP Optimization Suite 8.0](https://mlsanity.com/paper/2303.07101/) (2023)
- [A Single-Loop Gradient Descent and Perturbed Ascent Algorithm for Nonconvex Functional Constrained Optimization](https://mlsanity.com/paper/2207.05650/) (2022)
- [Moreau Envelope Augmented Lagrangian Method for Nonconvex Optimization with Linear Constraints](https://mlsanity.com/paper/2101.08519/) (2021)
- [Structured Hammerstein-Wiener Model Learning for Model Predictive Control](https://mlsanity.com/paper/2107.04247/) (2021)
- [SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs](https://mlsanity.com/paper/2106.13721/) (2021)

## Abstract (arXiv)

Traditional mathematical programming solvers require long computational times to solve constrained minimization problems of complex and large-scale physical systems. Therefore, these problems are often transformed into unconstrained ones, and solved with computationally efficient optimization approaches based on first-order information, such as the gradient descent method. However, for unconstrained problems, balancing the minimization of the objective function with the reduction of constraint violations is challenging. We consider the class of time-dependent minimization problems with increasing (possibly) nonlinear and non-convex objective function and non-decreasing (possibly) nonlinear and non-convex inequality constraints. To efficiently solve them, we propose a penalty-based guardrail algorithm (PGA). This algorithm adapts a standard penalty-based method by dynamically updating the right-hand side of the constraints with a guardrail variable which adds a margin to prevent violations. We evaluate PGA on two novel application domains: a simplified model of a district heating system and an optimization model derived from learned deep neural networks. Our method significantly outperforms mathematical programming solvers and the standard penalty-based method, and achieves better performance and faster convergence than a state-of-the-art algorithm (IPDD) within a specified time limit.