Wolfe duality and saddle point analysis on Riemannian manifolds for interval-valued optimization problems

A stabilized sequential quadratic programming method for degenerate nonlinear optimization problems on Riemannian manifolds

This study extends the stabilized SQP framework from Euclidean spaces to Riemannian manifolds and proves that the generated sequence has an accumulation point that is a Karush--Kuhn--Tucker (KKT) point, an approximate KKT (AKKT) point, or a stationary point of an associated feasibility problem.

Centered Weak Discrete Riemannian Gradients: A Unified Framework for Riemannian Optimization

We introduce the centered weak discrete Riemannian gradient (c-wDRG) framework for the unified analysis of optimization methods on Riemannian manifolds. The framework uses a center point to represent the relevant logarithmic differences in a common tangent space and covers Riemannian steepest descent, proximal point, p...

On Some Problems of Nonsmooth Analysis on Riemannian Manifolds

Semilinear Neumann boundary value problems for measure-valued maps

We study the Wasserstein lift of nonlinear Poisson systems with inhomogeneous Neumann boundary conditions. We establish the existence of minimizers using new estimates involving the $p$-moments of measure-valued traces. We also derive the optimality conditions, which turn out to be matrix-valued generalizations of pres...

Semilinear overdetermined problems, a divergence formula, and geometric inequalities

Considering an $n$-dimensional compact Riemannian manifold with a boundary that satisfies a Serrin-type problem, we prove sharp upper and lower bounds for the area of such a boundary. Then, we present the main result of this paper: a divergence formula for a special vector field on a given Riemannian manifold. This div...

Iteration of Complexity and Asymptotic Analysis of Gradient-Type Methods with Non-monotone Line Search on Riemannian Manifolds

This paper investigates gradient-type methods for solving optimization problems on Riemannian manifolds. In this approach, we utilize a search direction based on the gradient direction and employ a general non-monotone line search scheme to determine the stepsize at each iteration. This scheme encompasses several well-...