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In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems…
Multi-objective optimization is crucial in scientific and industrial applications where solutions must balance trade-offs among conflicting objectives. State-of-the-art methods, such as NSGA-III and MOEA/D, can handle many objectives but…
This work explores the ability of collective matrix factorization models in recommender systems to make predictions about users and items for which there is side information available but no feedback or interactions data, and proposes a new…
Decision trees are a popular machine learning model which are traditionally trained by heuristic methods. Massive improvements in computing power and optimisation techniques has led to renewed interest in learning globally optimal decision…
Skyline queries are one of the most widely adopted tools for Multi-Criteria Analysis, with applications covering diverse domains, including, e.g., Database Systems, Data Mining, and Decision Making. Skylines indeed offer a useful overview…
We are motivated by large scale submodular optimization problems, where standard algorithms that treat the submodular functions in the \emph{value oracle model} do not scale. In this paper, we present a model called the…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches.…
We consider single and multiobjective simulation-based optimization problems. Simulation-based optimization has traditionally used both model-based and search-based methods, often in isolation. Model-based methods include trust region…
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points,…
It is a crucial problem how to heat oil and save running cost for crude oil transport. This paper strictly formulates such a heated oil pipeline problem as a mixed integer nonlinear programming model. Nonconvex and convex continuous…
Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. However, the impact of the choice of the underlying scalarizing function(s) is still far from being well understood.…
We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
Although energy system optimisation based on linear optimisation is often used for influential energy outlooks and studies for political decision-makers, the underlying background still needs to be described in the scientific literature in…