In this work, we present an introduction to automatic differentiation, its use in optimization software, and some new potential usages. We focus on the potential of this technique in optimization. We do not dive deeply in the intricacies of automatic differentiation, but put forward its key ideas. We sketch a survey, as of today, of automatic differentiation software, but warn the reader that the situation with respect to software evolves rapidly. In the last part of the paper, we present some...

Se modeliza el problema no lineal de producción de carne de vacuno por Programación Geométrica Signomial. Los datos técnicos utilizados se han extraído del trabajo de Epplin y Heady (1984). Se aplican transformaciones inversas y métodos de condensación al problema signomial para simplificar el modelo teórico. Finalmente, se calcula la composición de la ración óptima, bajo distintas consideraciones y se comentan los resultados obtenidos, que confirman y completan otros experimentales ya existentes...

A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent...

The present paper studies the following constrained vector optimization problem: ${min}_{C}f\left(x\right)$, $g\left(x\right)\in -K$, $h\left(x\right)=0$, where $f:{ℝ}^n\to {ℝ}^m$, $g:{ℝ}^n\to {ℝ}^p$ are locally Lipschitz functions, $h:{ℝ}^n\to {ℝ}^q$ is $C^1$ function, and $C\subset {ℝ}^m$ and $K\subset {ℝ}^p$ are closed convex cones. Two types of solutions are important for the consideration, namely $w$-minimizers (weakly efficient points) and $i$-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point $x^0$ to be a $w$-minimizer and first-order sufficient conditions for $x^0$...