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We study almost minimizers for the thin obstacle problem with variable H\"older continuous coefficients and zero thin obstacle and establish their $C^{1,\beta}$ regularity on the either side of the thin space. Under an additional assumption…

Analysis of PDEs · Mathematics 2020-07-16 Seongmin Jeon , Arshak Petrosyan , Mariana Smit Vega Garcia

We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…

Statistics Theory · Mathematics 2015-01-05 Po-Ling Loh , Martin J. Wainwright

We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…

Optimization and Control · Mathematics 2026-05-04 Louis Shuo Wang

Minimizing a smooth function f on a closed subset C leads to different notions of stationarity: Fr{\'e}chet stationarity, which carries a strong variational meaning, and criticality, which is defined through a closure process and involves…

Optimization and Control · Mathematics 2024-11-05 Edouard Pauwels

We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…

Optimization and Control · Mathematics 2022-01-14 Christian Kirches , Jeffrey Larson , Sven Leyffer , Paul Manns

We study the power and limitations of component-stable algorithms in the low-space model of Massively Parallel Computation (MPC). Recently Ghaffari, Kuhn and Uitto (FOCS 2019) introduced the class of component-stable low-space MPC…

Data Structures and Algorithms · Computer Science 2021-06-04 Artur Czumaj , Peter Davies , Merav Parter

Numerous machine learning and industrial problems can be modeled as the minimization of a sum of $N$ so-called clipped convex functions (SCC), i.e. each term of the sum stems as the pointwise minimum between a constant and a convex…

Optimization and Control · Mathematics 2025-02-03 Guillaume Van Dessel , François Glineur

A completion of an m-by-n matrix A with entries in {0,1,*} is obtained by setting all *-entries to constants 0 or 1. A system of semi-linear equations over GF(2) has the form Mx=f(x), where M is a completion of A and f:{0,1}^n --> {0,1}^m…

Computational Complexity · Computer Science 2012-04-18 S. Jukna , G. Schnitger

This paper presents a novel model predictive control (MPC) formulation for set-point tracking. Stabilizing predictive controllers based on terminal ingredients may exhibit stability and feasibility issues in the event of a reference change…

Systems and Control · Electrical Eng. & Systems 2021-02-01 Pablo Krupa , Daniel Limon , Teodoro Alamo

The paper is devoted to an analysis of a new constraint qualification and a derivation of the strongest existing optimality conditions for nonsmooth mathematical programming problems with equality and inequality constraints in terms of…

Optimization and Control · Mathematics 2020-11-19 M. V. Dolgopolik

In this paper, a convergence proof for the recently proposed sparse possibilistic c-means (SPCM) algorithm is provided, utilizing the celebrated Zangwill convergence theorem. It is shown that the iterative sequence generated by SPCM…

Computer Vision and Pattern Recognition · Computer Science 2017-04-20 Spyridoula D. Xenaki , Konstantinos D. Koutroumbas , Athanasios A. Rontogiannis

If $N \subset P,Q \subset M$ are type II_1 factors with $N' \cap M = C id$ and $[M:N]$ finite we show that restrictions on the standard invariants of the elementary inclusions $N \subset P$, $N \subset Q$, $P \subset M$ and $Q \subset M$…

Operator Algebras · Mathematics 2007-05-23 Pinhas Grossman , Vaughan F. R. Jones

We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the Clarke tangent cone of the state constraint set is non-empty (this is the constraint…

Optimization and Control · Mathematics 2018-10-22 Nathalie Khalil , Sofia O. Lopes

Relaxed constant positive linear dependence constraint qualification (RCPLD) for a system of smooth equalities and inequalities is a constraint qualification that is weaker than the usual constraint qualifications such as Mangasarian…

Optimization and Control · Mathematics 2020-03-24 Mengwei Xu , Jane J. Ye

We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.

General Topology · Mathematics 2016-11-25 Hassen Aydi

This paper investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus…

Optimization and Control · Mathematics 2025-08-12 Nguyen Huy Chieu , Nguyen Thi Quynh Trang , Nguyen Thi Hai Yen

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

Functional Analysis · Mathematics 2009-06-12 José R. Morales , Edixon Rojas

In this article, we investigate some fixed point results satisfying a new generalized $\Delta$-implicit contractive condition in ordered complete multiplicative $\mathbf{G}_\mathcal{M}-$metric space. Also, some new definitions and fixed…

Functional Analysis · Mathematics 2022-06-14 Mohamed Gamal , Fu-Gui Shi

We prove the existence of common fixed points for two weakly compatible mappings satisfying a 'generalized condition (B)'. This result generalizes some theorems of Al-Thagafi and Shahzad \cite{AlThagafi2006} and Babu, Sandhya and Kameswari…

Functional Analysis · Mathematics 2025-08-26 Mujahid Abbas , G. V. R. Babu , Alemayehu G. Negash

We introduce a coinductive version of the well-foundedness of N that is used in our proof within minimal logic of the constructive counterpart CLNP to the standard least number principle LNP. According to CLNP, an inhabited complemented…

Logic · Mathematics 2025-07-02 Iosif Petrakis