Abstract. A family of integral functionals F which model in a simplified way material microstructure occupying a two-dimensional domain Ω and which take account of surface energy and a variable well depth is studied. It is shown that there is a critical well depth, whose scaling with the surface energy density and domain dimensions is given, below which the state u = 0 is the global minimizer o...

We prove that a certain class of elliptic free boundary problems, which includes the Prandtl–Batchelor problem from fluid dynamics as special case, has two distinct nontrivial solutions for large values parameter. The first solution is global minimizer energy. energy functional nondifferentiable, so standard variational arguments cannot be used directly to obtain second solution. our limit moun...

It has been shown that a global minimizer of smooth determinant matrix function corresponds to the largest cycle graph. When it exists, this is Hamiltonian cycle. Finding minimizers even challenge. The difficulty often exacerbated by existence many minimizers. One may think would help, but in case cycles ratio number local typically astronomically small. There are various equivalent forms probl...

Abtstract A generalization of the multistart algorithm is proposed for nding the global minimizer of a nonlinear function of n variables. Our method concentrates a quasirandom sample by performing a few inexpensive local searches. The sample is then reduced by replacing worse points by new quasirandom points. A complete local search is performed only on those points with small function values. ...

In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete applications such as dictionary learning, generalized phase retrieval, and orthogonal tensor decomposition are known to induce such structures. We describe a second-o...

This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differentia...

This paper extends the full convergence of the classic proximal point method to solve continuous quasiconvex minimization problems in Euclidian spaces. Under the assumption that the global minimizer set is nonempty we prove the full convergence of the sequence generated by the method to a certain generalized critical point of the problem.