arXiv subjects

Ademir Alves Ribeiro

Publications and source records attributed to Ademir Alves Ribeiro.

3 recordsLinked to original sources

arXiv2026

Fejér* monotonicity in optimization algorithms

Fejér monotonicity is a well-established property often observed in sequences generated by optimization algorithms. In this paper, we study an extension of this property, called Fejér* monotonicity, which was initially proposed in [SIAM J. Optim., 34(3), 2535-2556 (2024)]. We discuss and explore its behavior within Hilbert spaces as a tool for optimization algorithms. Additionally, we investigate weak and strong convergence properties of this novel concept. Through illustrative examples and insightful results, we contrast Fejér* with weaker notions of quasi-Fejér-type monotonicity.

math.OC↗

arXiv2022

On strong second-order optimality conditions under relaxed constant rank constraint qualification

We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification. This condition generalizes the so-called linear independence constraint qualification. Although the optimality conditions are well established in the literature, the proofs presented here are based solely on the well-known inverse function theorem. This is the only prerequisite from real analysis used to establish two auxiliary results needed to prove the optimality conditions, thereby making this paper totally self-contained.

math.OC↗

arXiv2019

Calculus, constrained minimization and Lagrange multipliers: Is the optimal critical point a local minimizer?

In this short note, we discuss how the optimality conditions for the problem of minimizing a multivariate function subject to equality constraints have been dealt with in undergraduate Calculus. We are particularly interested in the 2 or 3-dimensional cases, which are the most common cases in Calculus courses. Besides giving sufficient conditions to a critical point to be a local minimizer, we also present and discuss counterexamples to some statements encountered in the undergraduate literature on Lagrange Multipliers, such as `among the critical points, the ones which have the smallest image (under the function) are minimizers' or `a single critical point (which is a local minimizer) is a global minimizer'.

math.HO↗