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Saddle Points in Completely Regular Topological Spaces
We give a characterization of completely regular topological spaces. Applying some recent results for supinf problems in completely regular...
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Inertial Newton Algorithms Avoiding Strict Saddle Points
We study the asymptotic behavior of second-order algorithms mixing Newton’s method and inertial gradient descent in non-convex landscapes. We show...
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Saddle Points Problems
This chapter is devoted to the solution of saddle point problems that can be written in the abstract form...
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On formal normal forms of holomorphic germs at super-saddle fixed points
We consider a class of holomorphic skew product germs at super-saddle fixed points, which formally conjugate to their normal forms. We give necessary...
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Local saddle points for unconstrained polynomial optimization
This paper gives an algorithm for computing local saddle points for unconstrained polynomial optimization. It is based on optimality conditions and...
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Existence of Four-Crossing-Points Limit Cycles in Planar Sector-Wise Linear Systems with Saddle-Saddle Dynamics
In this paper, we study a family of planar piecewise linear systems with saddle-saddle dynamics and sector-wise separation, which is formed by two...
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A Fast and Simple Modification of Newton’s Method Avoiding Saddle Points
We propose in this paper New Q-Newton’s method. The update rule is conceptually very simple, using the projections to the vector subspaces generated...
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A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape
We propose a model-free shrinking-dimer saddle dynamics for finding any-index saddle points and constructing the solution landscapes, in which the...
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Stability of a Traveling Wave on a Saddle-Node Trajectory
AbstractFor semilinear partial differential equations, we consider the solution in the form of a plane wave traveling with a constant velocity. This...
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Error Estimate for Semi-implicit Method of Sphere-Constrained High-Index Saddle Dynamics
The authors prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics, which serves as a powerful...
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Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere
We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle...
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Robust Bond Portfolio Construction via Convex–Concave Saddle Point Optimization
The minimum (worst case) value of a long-only portfolio of bonds, over a convex set of yield curves and spreads, can be estimated by its...
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Global Manifolds of Saddle Periodic Orbits Parametrised by Isochrons
Global stable and unstable manifolds of a saddle periodic orbit of a vector field carry phase information of how trajectories on the manifold...
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Bifurcation Structure of Interval Maps with Orbits Homoclinic to a Saddle-Focus
We study homoclinic bifurcations in an interval map associated with a saddle-focus of (2, 1)-type in ℤ 2 -symmetric systems. Our study of this map...
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Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points,...
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Some saddle-point theorems for vector-valued functions
This paper concerns with vector saddle point problems where the image space of the objective bifunction is not endowed with any topology and the...
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A generalized relaxed block positive-semidefinite splitting preconditioner for generalized saddle point linear system
In this paper, based on the block positive-semidefinite splitting (BPS) preconditioner studied recently and the relaxation technique, a generalized...
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Active Learning for Saddle Point Calculation
The saddle point (SP) calculation is a grand challenge for computationally intensive energy function in computational chemistry area, where the...
