A Proximal-Type Method for Convex Vector Optimization Problem in Banach Spaces

Generalized Proximal Method for Efficient Solutions in Vector Optimization

“…It is worth noticing that the authors in [7,8] introduced and studied the so-called proximal-type and approximate generalized proximal-type (or generalized proximal) methods of finding weak efficient solutions to the convex vector optimization problem for a mapping from a uniformly convex and uniformly smooth Banach space to a real Banach space with the ordering cone C having a nonempty interior. Under some conditions, they proved that any sequence generated by their methods weakly converges to a weak efficient solution of the problem.…”

Shape space figure-8 solution of three body problem with two equal masses

“…• Level estimate: one gives a sharp lower bound estimate of the action functional among all the collision paths in the set of admissible paths and then try to find a collision-free test path within the set of admissible paths, whose action value is strictly smaller than the previous lower bound estimate. See [1][2][3]6].…”

“…At this moment, this seems hard to do. In general, level estimate used in [2] and [3] can give a good lower bound estimate of the action value of a collision path. However it is not the case when the collision path is collinear (all three masses stay on a single line all the time), which is exactly the case for a Schubart solution.…”

Inexact Proximal Point Methods in Metric Spaces

“…In a Hilbert space setting, convergence results for a nonconvex objective function were established in [13]. Convergence results in Banach spaces were obtained in [2,11,17,18,28]. Variable-metric methods were used in order to obtain convergence results in [1,7,22,24].…”