Related papers: On some global implicit function theorems for set-…
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…
Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit…
In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze…
We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these…
Many loss functions in representation learning are invariant under a continuous symmetry transformation. For example, the loss function of word embeddings (Mikolov et al., 2013) remains unchanged if we simultaneously rotate all word and…
This paper addresses the problem of modeling and estimating dynamic multi-valued mappings. While most mathematical models provide a unique solution for a given input, real-world applications often lack deterministic solutions. In such…
Paper contains description of the fields nonlinear modes successive quantization scheme. It is shown that the path integrals for absorption part of amplitudes are defined on the Dirac ($\d$-like) functional measure. This permits arbitrary…
In this paper, we remark on the published paper "Treatment of Set-Valued Robustness via Separation and Scalarization" [1], which deals with the robust solution to an uncertain constrained set-valued optimization problem via scalarization…
The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…
Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings,…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the…
We study the robustness of global post-hoc explanations for predictive models trained on tabular data. Effects of predictor features in black-box supervised learning are an essential diagnostic tool for model debugging and scientific…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
We investigate the computation of the gradient of the value function in parametric convex optimization problems. We derive general expression for the gradient of the value function in terms of the cost function, constraints and Lagrange…
Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…
Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task…
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…