Emergence of skyrmion lattices and bimerons in chiral magnetic thin films with nonmagnetic impurities

Skyrmions are topologically protected field structures with particlelike characteristics that play important roles in several areas of science. Recently, skyrmions have been directly observed in chiral magnets. Here, we investigate the effects of pointlike nonmagnetic impurities on the distinct initial states (random or helical ones) and on the formation of the skyrmion crystal in a discrete lattice. Using Monte Carlo techniques, we have found that even a small percentage of spin vacancies present in the chiral magnetic thin film considerably affects the skyrmion order. The main effects of impurities are somewhat similar to thermal effects. The presence of these spin vacancies also induces the formation of bimerons in both the helical and skyrmion states. We also investigate how adjacent impurities forming a hole affect the skyrmion crystal

New sequential optimality conditions for mathematical programs with complementarity constraints and algorithmic consequences

In recent years, the theoretical convergence of iterative methods for solving nonlinearnconstrained optimization problems has been addressed using sequential optimality conditions, which are satisfied by minimizers independently of constraint qualifications (CQs). Even though there is a considerable literature devoted to sequential conditions for standard nonlinear optimization, the same is not true for mathematical programs with complementarity constraints (MPCCs). In this paper, we show that the established sequential optimality conditions are not suitable for the analysis of convergence of algorithms for MPCC. We then propose new sequential optimality conditions for usual stationarity concepts for MPCC, namely, weak, Clarke, and Mordukhovich stationarity. We call these conditions AW-, AC-, and AM-stationarity, respectively. The weakest MPCC-tailored CQs associated with them are also provided. We show that some of the existing methods for MPCC reach AC-stationary points, extending previous convergence results. In particular, the new results include the linear case, not previously covered.29432013230CNPQ - Conselho Nacional de Desenvolvimento Científico e TecnológicoFAPESP – Fundação de Amparo à Pesquisa Do Estado De São Paulo301888/2017-5; 306986/2016- 7; 302915/2016-82013/07375-0; 2013/05475-7; 2017/18308-