On approximate antigradients

On Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras

We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

On Approximate Horn Minimization

The minimization problem for Horn formulas is to find a Horn formula equivalent to a given Horn formula, using a minimum number of clauses. A 2 1−ǫ(n)-inapproximability result is proven, which is the first non-trivial inapproximability result for this problem. We also consider several other versions of Horn minimization. The more general version which allows for the introduction of new variable...

On Approximate Dynamic Inversion

Approximate Dynamic Inversion has been established as a method to control minimum-phase, nonaffine-incontrol systems [1]. In this report, we re-state the main results of [1], clarify some minor notational errors, and prove the same results in an expanded form. In the large, the main results of [1] still stand. The development follows [1] closely, and no novelty is claimed herein. The purpose of...

On Approximate Non-Interference

Approximate Tradeoffs on Matroids

We consider problems where a solution is evaluated with a couple. Each coordinate of this couple represents an agent’s utility. Due to the possible conflicts, it is unlikely that one feasible solution is optimal for both agents. Then, a natural aim is to find tradeoffs. We investigate tradeoff solutions with guarantees for the agents.The focus is on discrete problems having a matroid structure....