A two-phase stochastic momentum-based algorithm for nonconvex expectation-constrained optimization
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Subgradient Convergence Implies Subdifferential Convergence on Weakly Convex Functions: With Uniform Rates Guarantees
In nonsmooth, nonconvex stochastic optimization, understanding the uniform convergence of subdifferential mappings is crucial for analyzing stationary points of sample average approximations of risk as they approach the population risk. Yet, characterizing this convergence remains a fundamental challenge. This work introduces a novel perspective by connecting the uniform convergence of subdifferential mappings to that of subgradient … Read more
Optimal Sports League Realignment
We consider approaches for optimally organizing competitive sports leagues in light of competitive and logistical considerations. A common objective is to assign teams to divisions so that intradivisional travel is minimized. We present a bilinear programming formulation based on k-way equipartitioning, and show how this formulation can be extended to account for additional constraints and … Read more
On the global convergence of a general class of augmented Lagrangian methods
In [E. G. Birgin, R. Castillo and J. M. Martínez, Computational Optimization and Applications 31, pp. 31-55, 2005], a general class of safeguarded augmented Lagrangian methods is introduced which includes a large number of different methods from the literature. Besides a numerical comparison including 65 different methods, primal-dual global convergence to a KKT point is … Read more
Mixed-Integer Linear Optimization for Cardinality-Constrained Random Forests
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 are only accessible for a proper subset of the given … Read more
Exploiting Sign Symmetries in Minimizing Sums of Rational Functions
This paper is devoted to the problem of minimizing a sum of rational functions over a basic semialgebraic set. We provide a hierarchy of sum of squares (SOS) relaxations that is dual to the generalized moment problem approach due to Bugarin, Henrion, and Lasserre. The investigation of the dual SOS aspect offers two benefits: 1) … Read more
Approaches to iterative algorithms for solving nonlinear equations with an application in tomographic absorption spectroscopy
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with variables coupling, we consider a situation where straightforward translation to a fixed point problem is not possible because the operators that represent the … Read more
Considering homeowner acceptance of retrofit measures within energy supply network optimization
A key factor towards a low-carbon society is energy efficient heating of private houses. The choice of heating technology as well as the decision for certain energy-efficient house renovations are made mainly by individual homeowners. In contrast, municipal energy network planning heavily depends on and strongly affects these decisions. Further, there are different conflicting objectives … Read more
Detecting and Handling Reflection Symmetries in Mixed-Integer (Nonlinear) Programming
Symmetries in mixed-integer (nonlinear) programs (MINLP), if not handled appropriately, are known to negatively impact the performance of (spatial) branch-and-bound algorithms. Usually one thus tries to remove symmetries from the problem formulation or is relying on a solver that automatically detects and handles symmetries. While modelers of a problem can handle various kinds of symmetries, … Read more
Multistage Stochastic Facility Location under Facility Disruption Uncertainty
We consider a multistage variant of the classical stochastic capacitated facility location problem under facility disruption uncertainty. Two solution algorithms for this problem class are presented: (1) stochastic dual dynamic integer programming (SDDiP), the state-of-the-art algorithm for solving multistage stochastic integer programs, and (2) shadow price approximation (SPA), an algorithm utilizing trained parameters of the … Read more