Héctor Ramírez

Facial approach for constructing stationary points for mathematical programs with cone complementarity constraints

  • Javier I. Madariaga
  • Héctor Ramírez
    • Categories Complementarity and Variational Inequalities, Cone Programming Tags , , ,

    This paper studies stationary points in mathematical programs with cone complementarity constraints (CMPCC). We begin by reviewing various formulations of CMPCC and revisiting definitions for Bouligand, proximal strong, regular strong, Wachsmuth’s strong, L-strong, weak, as well as Mordukhovich and Clarke stationary points, establishing a comprehensive framework for CMPCC. Building on key principles related to cone … Read more

    A minimal face constant rank constraint qualification for reducible conic programming

  • Roberto Andreani
  • Gabriel Haeser
  • leomakoto
  • Héctor Ramírez
    • Categories Cone Programming, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , ,

    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 programming under a constant rank condition. Mathematical Programming, 2023. DOI: 10.1007/s10107-023-01942-8] we introduced a constant rank constraint qualification for nonlinear semidefinite and second-order cone programming by considering all faces … Read more

    Global Convergence of Algorithms Under Constant Rank Conditions for Nonlinear Second-Order Cone Programming

  • Roberto Andreani
  • Gabriel Haeser
  • Leonardo M. Mito
  • Héctor Ramírez
  • Thiago P. Silveira
    • Categories Constrained Nonlinear Optimization, Second-Order Cone Programming Tags , , , ,

    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 nondegeneracy (or transversality) and Robinson’s constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of the problem, namely, its eigendecomposition. This allows formulating the … Read more

    First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition

  • Roberto Andreani
  • Gabriel Haeser
  • Héctor Ramírez
  • Leonardo M. Mito
  • Thiago P. Siqueira
    • Categories Constrained Nonlinear Optimization, Second-Order Cone Programming, Semi-definite Programming

    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 context by exploiting the eigenvector structure of the problem. In this paper we propose a more general and geometric approach for defining a new extension of this condition to the … Read more

    Sequential constant rank constraint qualifications for nonlinear semidefinite programming with applications

  • Roberto Andreani
  • Gabriel Haeser
  • Héctor Ramírez
  • Leonardo M. Mito
    • Categories Constrained Nonlinear Optimization, Second-Order Cone Programming, Semi-definite Programming Tags , , ,

    We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global convergence proof of a class of algorithms to stationary points without assuming neither uniqueness of the Lagrange multiplier nor boundedness of the Lagrange … Read more

    Weak notions of nondegeneracy in nonlinear semidefinite programming

  • Roberto Andreani
  • Gabriel Haeser
  • Leonardo M. Mito
  • Héctor Ramírez
    • Categories Constrained Nonlinear Optimization, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

    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 any fixed orthonormal basis of the, let us say, $\ell$-dimensional kernel of the constraint matrix, by the linear independence of a set of $\ell(\ell+1)/2$ derivative vectors. We show that this … Read more

    Naive constant rank-type constraint qualifications for multifold second-order cone programming and semidefinite programming

  • Roberto Andreani
  • Gabriel Haeser
  • Héctor Ramírez
  • Leonardo M. Mito
  • Daiana O. Santos
  • Thiago P. Siqueira
    • Categories Linear, Cone and Semidefinite Programming

    The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the derivative of the value function. In this paper we discuss naive extensions of constant rank-type constraint qualifications to second-order cone programming and semidefinite programming, … Read more

    Second-Order Variational Analysis in Conic Programming with Applications to Optimality and Stability

  • Boris S. Mordukhovich
  • Jiri V. Outrata
  • Héctor Ramírez
    • Categories Convex and Nonsmooth Optimization Tags , , , , , ,

    This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized di erential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues related … Read more

    Linear complementarity problems over symmetric cones: Characterization of Qb-transformations and existence results

  • Julio López
  • Héctor Ramírez
  • Rubén López
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    This paper is devoted to the study of the {symmetric cone linear complementarity problem} (SCLCP). In this context, our aim is to characterize the class Q_b in terms of larger classes, such as Q and R_0. For this, we introduce the class F and García’s transformations. We studied them for concrete particular instances (such as … Read more