Related papers: Around a Farkas type Lemma
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…
The aim of this paper is to implement some new techniques, based on conjugate duality in convex optimization, for proving the existence of global error bounds for convex inequality systems. We deal first of all with systems described via…
Program termination is a hot research topic in program analysis. The last few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These…
We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting…
Transparency is an essential requirement of machine learning based decision making systems that are deployed in real world. Often, transparency of a given system is achieved by providing explanations of the behavior and predictions of the…
Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions,…
This paper gives two different proofs to a structural theorem of decreasing minimization (lexicographic optimization) on integrally convex sets. The theorem states that the set of decreasingly minimal elements of an integrally convex set…
We introduce a constraint qualification condition (GPMFCQ) for smooth infinite programming problems, where the nonlinear operator defining the equality constraints has nonsurjective derivative at the local minimum. The condition is a…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…
In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent…
In this paper, we study constraint qualifications for the nonconvex inequality defined by a proper lower semicontinuous function. These constraint qualifications involve the generalized construction of normal cones and subdifferentials.…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
The main purpose of this note is to prove an upper bound on the number of lattice points of a centrally symmetric convex body in terms of the successive minima of the body. This bound improves on former bounds and narrows the gap towards a…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
The aim of this paper is to give two complete and simple characterizations of Minkowski norms N on an arbitrary topological real vector space such that the sublevel sets of N are strictly convex. We first show that this property is…
We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…
Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas' lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas' lemma from it using…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…
Interpretable Machine Learning faces a recurring challenge of explaining the predictions made by opaque classifiers such as ensemble models, kernel methods, or neural networks in terms that are understandable to humans. When the model is…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…