In this work we present a new restart technique for iterative projection methods for nonlinear eigenvalue problems admitting minmax characterization of their eigenvalues. Our technique makes use of the minmax induced local enumeration of the eigenvalues in the inner iteration. In contrast to global numbering which requires including all the previously computed eigenvectors in the search subspac...

We consider approximation of the optimal Yen algorithm for interpolation from a nonuniformly-spaced grid. Although the Yen interpolator is optimal in many senses, it suffers from severe numerical ill conditioning. We suggest a tradeoff between accuracy in computing the interpolator and accuracy in performing the interpolation. A new interpolator is proposed using Choi’s expression for interpola...

In the present paper, two types of second order dual models are formulated for a minmax fractional programming problem. The concept of η-bonvexity/ generalized η-bonvexity is adopted in order to discuss weak, strong and strict converse duality theorems.

We show that for any discount factor, there is a natural number M such that all subgame perfect outcomes of the discounted repeated prisoners’ dilemma (pure strategies) can be obtained by subgame perfect strategies with the following property: current play depends only on the number of the time-index and on the history of the last M periods. This strong result, however, does not suffice to esta...

This paper proposes Friedrichs learning as a novel deep methodology that can learn the weak solutions of PDEs via minmax formulation, which transforms PDE problem into minimax optimization to identify solutions. The name "Friedrichs learning" is for highlighting close relationship between our strategy and theory on symmetric systems PDEs. solution test function in formulation are parameterized ...

We address the problem of robust decision making for stochastic network design. Our work is motivated by spatial conservation planning where the goal is to take management decisions within a fixed budget to maximize the expected spread of a population of species over a network of land parcels. Most previous work for this problem assumes that accurate estimates of different network parameters (e...

Both questions ask about some form of optimality. The first one is about optimality of an estimator, whereas the second one is about optimality of a bound. The difficulty of these questions varies depending on whether we are looking for a positive or a negative answer. Indeed, a positive answer to these questions simply consists in finding a better proof for the estimator we have studied (quest...