The Higgs potential of 2HDM keeps its generic form under the group of transformation GL(2, C), which is larger than the usually considered reparametrization group SU(2). This reparametrization symmetry induces the Minkowski space structure in the orbit space of 2HDM. Exploiting this property, we present a geometric analysis of the number and properties of stationary points of the most general 2...

The classical result on singularities for the 3D Navier-Stokes equations says that the 1-dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time t, with probability one the set of singular points is empty. The same result is true for a.e. initial condition wit...

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Conv...

This paper studies theoretical and practical properties of interior-penalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is shown to be globally convergent to strongly stationary points, under standard assumptions. These re...

We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of [Formula: see text]-stationarity (Benko and Gfrerer in Optimization 66(1):61-92, 2017). We demonstrate how [Formula: see text]-stationary solutions of the quadratic program ...

The stationary points of the potential energy function of the φ⁴ model on a two-dimensional square lattice with nearest-neighbor interactions are studied by means of two numerical methods: a numerical homotopy continuation method and a globally convergent Newton-Raphson method. We analyze the properties of the stationary points, in particular with respect to a number of quantities that have bee...

This paper is concerned with the study of necessary and sufficient optimality conditions for convex–concave generalized fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn–Tucker Saddle and Stationary points are characterized. In addition, some important theorems related...

In [3], an 2-active set algorithm was proposed for solving a mathematical program with a smooth objective function and linear inequality/complementarity constraints. It is asserted therein that, under a uniform LICQ on the 2-feasible set, this algorithm generates iterates whose cluster points are B-stationary points of the problem. However, the proof has a gap and only shows that each cluster p...

Reformulations of a generalization of a second-order cone complementarity problem (GSOCCP) as optimization problems are introduced, that preserve differentiability. Equivalence results are proved in the sense that the global minimizers of the reformulations with zero objective value are solutions to the GSOCCP and vice versa. Since the optimization problems involved include only simple constrai...

The connection between isobaric fragility and the properties of high-order stationary points of the potential energy surface in different supercooled Lennard-Jones mixtures was investigated. The increase of effective activation energies upon supercooling appears to be driven by the increase of average potential energy barriers measured by the energy dependence of the fraction of unstable modes....