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Input convex neural networks as surrogates in mathematical optimisation
Yu Liu, Jan Kronqvist, Fabricio Oliveira
Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research. The prevailing approach uses feedforward neural netw…
Separation, Constraint Qualifications, and Cycling in Outer Approximation
Erik Tamm, Jan Kronqvist
The outer approximation algorithm is a widely used method for solving convex mixed-integer nonlinear programs. While the algorithm is well established in theory and practice, certa…
A Framework for Eliminating Paradoxical Orders in European Day-Ahead Electricity Markets through Mixed-Integer Linear Programming Strong Duality
Zhen Wang, Mohammad Reza Hesamzadeh, Shudian Zhao +1
The presence of integer variables in the European day-ahead electricity market renders the social welfare maximization problem non-convex and non-differentiable, making classical m…
Warm-starting outer approximation for parameterized convex MINLP
Erik Tamm, Gabriele Eichfelder, Jan Kronqvist
We address the challenge of efficiently solving parameterized sequences of convex Mixed-Integer Nonlinear Programming (MINLP) problems through warm-starting techniques. We focus on…
A cutting plane algorithm for globally solving low dimensional k-means clustering problems
Martin Ryner, Jan Kronqvist, Johan Karlsson
Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approxima…
Solution Polishing via Path Relinking for Continuous Black-Box Optimization
Dimitri Papageorgiou, Jan Kronqvist, Asha Ramanujam +3
When faced with a limited budget of function evaluations, state-of-the-art black-box optimization (BBO) solvers struggle to obtain globally, or sometimes even locally, optimal solu…