On a threshold descent method for quasi-equilibria

A descent method for explicit computations on curves

‎It is shown that the knowledge of a surjective morphism $Xto Y$ of complex‎ ‎curves can be effectively used‎ ‎to make explicit calculations‎. ‎The method is demonstrated‎ ‎by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve ‎with period lattice $(1,tau)$‎, ‎the period matrix for the Jacobian of a family of genus-$2$ curves‎ ‎complementing the classi...

A Descent Resolvent Method for Mixed Quasi Variational Inequalities

In this paper, we suggest and analyze a new iterative method for solving mixed quasi variational inequalities. The new iteration is obtained by searching the optimal step size along the integrated descent direction from two descent directions. Global convergence of the proposal method is proved under certain assumptions. Our results can be treated as refinement of previously known results. An e...

Descent for Quasi-coherent Sheaves on Stacks

We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site C. We use this to prove homotopy invariance and generalized descent statements for categories of sheaves and quasi-coherent sheaves. As a corollary we obtain an alternate proof of a generalized change of rings theorem of Hovey.

Quasi Equilibria for Growth Economies

Gap functions for quasi-equilibria

An approach for solving quasi-equilibrium problems (QEPs) is proposed relying on gap functions, which allow reformulating QEPs as global optimization problems. The (generalized) smoothness properties of a gap function are analysed and an upper estimates of its Clarke directional derivative is given. Monotonicity assumptions on both the equilibrium and constraining bifunctions are a key tool to ...