7 citations · 29 across the 17 of their papers we have counts for
17 papers
Exploiting cone approximations in an augmented Lagrangian method for conic optimization
Mituhiro Fukuda, Walter Gómez, Gabriel Haeser +1
We propose an algorithm for general nonlinear conic programming which does not require the knowledge of the full cone, but rather a simpler, more tractable, approximation of it. We…
A simple proof of existence of Lagrange multipliers
Gabriel Haeser, Daiana Oliveira dos Santos
In the seminal book Méchanique analitique, Lagrange, 1788, the notion of a Lagrange multiplier was first introduced in order to study a smooth minimization problem subject to equal…
A semi-smooth Newton method for general projection equations applied to the nearest correlation matrix problem
Nicolas F. Armijo, Yunier Bello-Cruz, Gabriel Haeser
In this paper, we extend and investigate the properties of the semi-smooth Newton method when applied to a general projection equation in finite dimensional spaces. We first presen…
Constraint qualifications and strong global convergence properties of an augmented Lagrangian method on Riemannian manifolds
Roberto Andreani, Kelvin Rodrigues Couto, Orizon Pereira Ferreira +1
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…
A minimal face constant rank constraint qualification for reducible conic programming
Roberto Andreani, Gabriel Haeser, Leonardo M. Mito +1
In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ramírez, T. P. Silveira. First- and second-order optimality conditions for second-order cone and semidefinite programmin…
A Jacobi-type Newton method for Nash equilibrium problems with descent guarantees
Oliver Kolossoski, Luís Felipe Bueno, Gabriel Haeser
A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton's method to the system of nonlinear equations obtain…
On the weak second-order optimality condition for nonlinear semidefinite and second-order cone programming
Ellen H. Fukuda, Gabriel Haeser, Leonardo M. Mito
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built under nondegeneracy and strict c…
On the convergence of iterative schemes for solving a piecewise linear system of equations
Nicolas F. Armijo, Yunier Bello-Cruz, Gabriel Haeser
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic…
Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming
Roberto Andreani, Gabriel Haeser, Héctor Ramírez C. +2
In [R. Andreani, G. Haeser, L. M. Mito, H. Ramírez C., Weak notions of nondegeneracy in nonlinear semidefinite programming, arXiv:2012.14810, 2020] the classical notion of nondegen…
First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition
Roberto Andreani, Gabriel Haeser, Leonardo M. Mito +2
The well known constant rank constraint qualification [Math. Program. Study 21:110--126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic c…
Sequential constant rank constraint qualifications for nonlinear semidefinite programming with applications
Roberto Andreani, Gabriel Haeser, Leonardo M. Mito +1
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an ap…
Weak notions of nondegeneracy in nonlinear semidefinite programming
Roberto Andreani, Gabriel Haeser, Leonardo M. Mito +1
The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of a…
Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming
R. Andreani, G. Haeser, L. M. Mito +3
The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first-…
On the behavior of Lagrange multipliers in convex and non-convex infeasible interior point methods
Gabriel Haeser, Oliver Hinder, Yinyu Ye
We analyze sequences generated by interior point methods (IPMs) in convex and nonconvex settings. We prove that moving the primal feasibility at the same rate as the barrier parame…
On a conjecture in second-order optimality conditions
R. Behling, G. Haeser, A. Ramos +1
In this paper we deal with optimality conditions that can be verified by a nonlinear optimization algorithm, where only a single Lagrange multiplier is avaliable. In particular, we…
An extension of Yuan's Lemma and its applications in optimization
Gabriel Haeser
We prove an extension of Yuan's Lemma to more than two matrices, as long as the set of matrices has rank at most 2. This is used to generalize the main result of [A. Baccari and A.…
Optimality condition and complexity analysis for linearly-constrained optimization without differentiability on the boundary
Gabriel Haeser, Hongcheng Liu, Yinyu Ye
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By ex…