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

• URL: http://arxiv.org/abs/2405.01984v1
• Date: Fri, 3 May 2024 10:37:34 GMT
• Title: A Penalty-Based Guardrail Algorithm for Non-Decreasing Optimization with Inequality Constraints
• Authors: Ksenija Stepanovic, Wendelin Böhmer, Mathijs de Weerdt,
• Abstract summary: Traditional mathematical programming solvers require long computational times to solve constrained minimization problems. We propose a penalty-based guardrail algorithm (PGA) to efficiently solve them.
• Score: 1.5498250598583487
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Constrained Bi-Level Optimization: Proximal Lagrangian Value function Approach and Hessian-free Algorithm [8.479947546216131]
  We develop a Hessian-free gradient-based algorithm-termed proximal Lagrangian Value function-based Hessian-free Bi-level Algorithm (LV-HBA) LV-HBA is especially well-suited for machine learning applications.
  arXiv  Detail & Related papers  (2024-01-29T13:50:56Z)
• Optimizing NOTEARS Objectives via Topological Swaps [41.18829644248979]
  In this paper, we develop an effective method for a set of candidate algorithms. At the inner level, given a subject, we utilize off-the-the-art constraints. The proposed method significantly improves the score of other algorithms.
  arXiv  Detail & Related papers  (2023-05-26T21:49:37Z)
• Infeasible Deterministic, Stochastic, and Variance-Reduction Algorithms for Optimization under Orthogonality Constraints [9.301728976515255]
  This article provides new practical and theoretical developments for the landing algorithm. First, the method is extended to the Stiefel manifold. We also consider variance reduction algorithms when the cost function is an average of many functions.
  arXiv  Detail & Related papers  (2023-03-29T07:36:54Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [73.2273449996098]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms. An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Simultaneously Achieving Sublinear Regret and Constraint Violations for Online Convex Optimization with Time-varying Constraints [26.473560927031176]
  We develop a novel virtual-queue-based online algorithm for online convex optimization (OCO) problems with long-term and time-varying constraints. Our algorithm is the first parameter-free algorithm to simultaneously achieve sublinear dynamic regret and constraint violations.
  arXiv  Detail & Related papers  (2021-11-15T12:23:31Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• On Constraints in First-Order Optimization: A View from Non-Smooth Dynamical Systems [99.59934203759754]
  We introduce a class of first-order methods for smooth constrained optimization. Two distinctive features of our approach are that projections or optimizations over the entire feasible set are avoided. The resulting algorithmic procedure is simple to implement even when constraints are nonlinear.
  arXiv  Detail & Related papers  (2021-07-17T11:45:13Z)
• An Asymptotically Optimal Primal-Dual Incremental Algorithm for Contextual Linear Bandits [129.1029690825929]
  We introduce a novel algorithm improving over the state-of-the-art along multiple dimensions. We establish minimax optimality for any learning horizon in the special case of non-contextual linear bandits.
  arXiv  Detail & Related papers  (2020-10-23T09:12:47Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• Conditional gradient methods for stochastically constrained convex minimization [54.53786593679331]
  We propose two novel conditional gradient-based methods for solving structured convex optimization problems. The most important feature of our framework is that only a subset of the constraints is processed at each iteration. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees.
  arXiv  Detail & Related papers  (2020-07-07T21:26:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.