We study the structure of isometries of the quadratic Wasserstein space W2(Sn, · )over the sphere endowed with the distance inherited from the norm of Rn+1. We prove that W2(Sn, · )is isometrically rigid, meaning that its isometry group is isomorphic to that of (Sn, · ). This is in striking...

We generalize the results of Kuwae–Shioya and Bačák on Mosco convergence established for CAT(0)-spaces to the CAT(1)-setting, so that Mosco convergence implies convergence of resolvents which in turn imply convergence of gradient flows for lower-semicontinuous semi-convex functions. Our...

Sturm’s strong law of large numbers in CAT(0) spaces and in the Thompson metric space of positive invertible operators is not only an important theoretical generalization of the classical strong law but also serves as a root-finding algorithm in the spirit of a proximal point method with...

In recent decades, financialization has emerged as a significant phenomenon shaping global economies. It refers to the increasing role of financial markets, institutions, and practices in the overall functioning of economies, often at the expense of the real economy. The purpose of the study is...

We present an interior-point algorithmic framework for P_* (κ)-Linear Complementarity Problems that is based on a barrier function which is defined by a new class of univariate kernel functions called Standard Kernel Functions (SKFs). A unified, comprehensive complexity analysis of the generic...

In this paper, we revisit the main principles for constructing polynomial-time primal-dual interior-point algorithms (IPAs). Starting from the break-through paper by Gonzaga (1989), their development was related to the barrier methods, where the objective function was added to the barrier for...