Rafael Correa

Convergence of some algorithms for convex minimization

We present a simple and unified technique to establish convergence of various minimization methods. These contain the (conceptual) proximal point method, as well as implementable forms such as bundle algorithms, including the classical subgradient relaxation algorithm with divergent series.

A Global Algorithm for Nonlinear Semidefinite Programming

In this paper we propose a global algorithm for solving nonlinear semidefinite programming problems. This algorithm, inspired by the classic SQP (sequentially quadratic programming) method, modifies the S-SDP (sequentially semidefinite programming) local method by using a nondifferentiable merit function combined with a line search strategy.

Sub differential Monotonicity as Characterization of Convex Functions

We prove that a lower semicontinuous function defined on a Banach space is convex if and only if its subdifferential ismonotone.

An Algorithm for Global Minimization of Linearly Constrained Quadratic Functions

A branch and bound algorithm is proposed for finding an approximate global optimum of quadratic functions over a bounded polyhedral set. The algorithm uses Lagrangian duality to obtain lower bounds. Preliminary computational results are reported.

Primal and Dual Stability Results for Variational Inequalities

The purpose of this paper is to study the continuous dependence of solutions of variational inequalities with respect to perturbations of the data that are maximal monotone operators and closed convex functions. The constraint sets are defined by a finite number of linear equalities and non linear convex inequalities. Primal and dual stability results are given, extending the classical ones for optimization problems.

On Brøndsted–Rockafellar’s Theorem for convex lower semicontinuous epi-pointed functions in locally convex spaces

In this work we give an extension of the Brøndsted–Rockafellar Theorem, and some of its important consequences, to proper convex lower-semicontinuous epi-pointed functions defined in locally convex spaces. We use a new approach based on a simple variational principle, which also allows recovering the classical results in a natural way.

Various Lipschitz-like Properties for Functions and Sets I: Directional Derivative and Tangential Characterizations

In this work we introduce for extended real valued functions, defined on a Banach space

On the Klee--Saint Raymond's Characterization of Convexity

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Towards Supremum-Sum Subdifferential Calculus Free of Qualification Conditions

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Eigenvalue Localization for Multivalued Operators

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