We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e. , simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We prove that using absolute approximations of the players’...

Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential mixed-integer linearization with trust region safeguard,...

Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classify a new given point. In some scenarios, however, labels...

This paper studies stochastic optimization problems and associated Bellman equations in formats that allow for reduced dimensionality of the cost-to-go functions. In particular, we study stochastic control problems in the “decision-hazard-decision” form where at each stage, the system state...

The Chambolle–Pock method is a versatile three-parameter algorithm designed to solve a broad class of composite convex optimization problems, which encompass two proper, lower semicontinuous, and convex functions, along with a linear operator L . The functions are accessed via their proximal...

We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (SIAM J Optim 32:152–172, 2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an adjustable robust solution of a...

In 1964, Polyak showed that the Heavy-ball method, the simplest momentum technique, accelerates convergence of strongly-convex problems in the vicinity of the solution. While Nesterov later developed a globally accelerated version, Polyak's original algorithm remains simpler and more widely used...

We propose a gradient-based method to solve quasiconvex optimization problems through decomposed optimization and prove local superlinear convergence under mild regularity assumptions at the optimal solution. A practical implementation further provides global convergence while maintaining the...

It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and without coupling constraints w.r.t. their...

Bilevel problems are used to model the interaction between two decision makers in which the lower-level problem, the so-called follower's problem, appears as a constraint in the upper-level problem of the so-called leader. One issue in many practical situations is that the follower's problem is...