A Robust Optimization Framework for Wildfire Fuel Management
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robust optimization
Robust optimality for nonsmooth mathematical programs with equilibrium constraints under data uncertainty
We develop a unified framework for robust nonsmooth optimization problems with equilibrium constraints (UNMPEC). As a foundation, we study a robust nonsmooth nonlinear program with uncertainty in both the objective function and the inequality constraints (UNP). Using Clarke subdifferentials, we establish Karush–Kuhn–Tucker (KKT)–type necessary optimality conditions under an extended no–nonzero–abnormal–multiplier constraint qualification (ENNAMCQ). When the … Read more
A guided tour through the zoo of paired optimization problems
Many mathematical models base on the coupling of two or more optimization problems. This paper surveys possibilities to couple two optimization problems and discusses how solutions of the different models are interrelated with each other. The considered pairs stem from the fields of standard and generalized Nash equilibrium problems, optimistic and pessimistic bilevel problems, saddle … Read more
Towards robust optimal control of chromatographic separation processes with controlled flow reversal
Column liquid chromatography is an important technique applied in the production of biopharmaceuticals, specifically for the separation of biological macromolecules such as proteins. When setting up process conditions, it is crucial that the purity of the product is sufficiently high, even in the presence of perturbations in the process conditions, e.g., altered buffer salt concentrations. … Read more
Machine Learning Algorithms for Improving Black Box Optimization Solvers
Black-box optimization (BBO) addresses problems where objectives are accessible only through costly queries without gradients or explicit structure. Classical derivative-free methods—line search, direct search, and model-based solvers such as Bayesian optimization—form the backbone of BBO, yet often struggle in high-dimensional, noisy, or mixed-integer settings. Recent advances use machine learning (ML) and reinforcement learning (RL) to … Read more
Responsible Machine Learning via Mixed-Integer Optimization
In the last few decades, Machine Learning (ML) has achieved significant success across domains ranging from healthcare, sustainability, and the social sciences, to criminal justice and finance. But its deployment in increasingly sophisticated, critical, and sensitive areas affecting individuals, the groups they belong to, and society as a whole raises critical concerns around fairness, transparency … Read more
Solving Decision-Dependent Robust Problems as Bilevel Optimization Problems
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor exploited computationally. Based on the recent results by Goerigk et al. (2025), this paper is the first one that reformulates a given strictly robust optimization … Read more
Addressing Estimation Errors through Robust Portfolio Optimization
It is well known that the performance of the classical Markowitz model for portfolio optimization is extremely sensitive to estimation errors on the expected asset returns. Robust optimization mitigates this issue. We focus on ellipsoidal uncertainty sets around a point estimate of the expected asset returns. An important issue is the choice of the parameters … Read more
Correction to: A Lagrangian dual method for two-stage robust optimization with binary uncertainties
We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in Subramanyam (2022). We first present a simple counterexample where the original conditions are insufficient, highlight where the original proof fails, and then provide modified conditions along with a correct proof of their validity. Finally, although … Read more
Robust Appointment Scheduling for General Convex Uncertainty Sets
The Appointment Scheduling Problem (ASP) involves scheduling a finite number of customers with uncertain service times, served consecutively by a single server, with the goal of minimizing the weighted costs of waiting time, idle time, and overtime. Previous studies employing stochastic programming were limited to small instances or constrained by restrictive assumptions. We introduce a … Read more