In this paper we consider a vector-valued Allen-Cahn MPEC problem. To derive optimality conditions we exploit a regularization-relaxation technique. The optimality system of the regularized-relaxed subproblems are investigated by applying the classical result of Zowe and Kurcyusz. Finally we show that the stationary points of the regularizedrelaxed subproblems converge to weak stationary points...

A nonlinear least squares formulation for the maximum weight clique problem is proposed. When nonnegativity of variables is relaxed, it becomes possible to enumerate its stationary points assuming the degeneracy did not occur. It is proved that those stationary points are sufficient to recognize certain types of maximal cliques.

We give stationary point theorems of set-valued mappings in complete and compact metric spaces. The results in this note generalize a few results due to Fisher. 2000 Mathematics Subject Classification. 54H25.

We present a numerically stable way to compute oscillatory integrals of the form ∫ 1 −1 f(x)e iωg(x) dx. For each additional frequency, only a small, well-conditioned linear system with a Hessenberg matrix must be solved, and the amount of work needed decreases as the frequency increases. Moreover, we can modify the method for computing oscillatory integrals with stationary points. This is the ...

*Correspondence: [email protected] 1Dpto. de Análisis Matemático, IMUS (Instituto Matemático de la Universidad de Sevilla), Universidad de Sevilla, C/Tarfia s/n, 41012 Sevilla, Spain Full list of author information is available at the end of the article Abstract In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of...

A meth~ fi~r the hmalization, characterizadcm and ctnnputatitm of the stationary ptfints of a cxmtinutatsly differentiable real-valued fimction tff n variables is presented. It is based on the annbinatoriai topohgy concept of the degree of a mapping associated with an oriented polyhednm. The method consists of two principal steps: (i) Iocalizati, m (and am~putation if required) of a ~ationary p...

Five nontrivial stationary points are found for maximal gauged N=16 supergravity in three dimensions with gauge group SO(8) × SO(8) by restricting the potential to a submanifold of the space of SU (3) ⊂ (SO(8) × SO(8)) diag singlets. The construction presented here uses the embedding of E 7(+7) ⊂ E 8(+8) to lift the analysis of N = 8, D = 4 supergravity performed by N. Warner to N = 16, D = 3, ...

We propose a new algorithm for the nonlinear inequality constrained minimization problem, and prove that it generates a sequence converging to points satisfying the KKT second order necessary conditions for optimality. The algorithm is a line search algorithm using directions of negative curvature and it can be viewed as a non trivial extension of corresponding known techniques from unconstrain...

Necessary and sufficient conditions for the existence of common stationary points of two multivalued mappings and common stationary point theorems for multivalued mappings on bounded metric spaces are given. Our results extend the theorems due to Fisher in 1979, 1980, and 1983 and Ohta and Nikaido in 1994.

The double-covering map udc : R 2 → R is given by udc(x) = 1 √ 2|x| ( x2 2 − x12 2x1x2 ) in cartesian coordinates. This paper examines the conjecture that udc is the global minimizer of the Dirichlet energy I(u) = ∫ B |∇u| dx among allW 1,2 mappings u of the unit ball B ⊂ R satisfying (i) u = udc on ∂B, and (ii) det∇u = 1 almost everywhere. Let the class of such admissible maps be A. The chief ...