A thermoviscoplastic model with linear kinematic hardening, von Mises yield condition and mixed boundary conditions is considered. The existence of a unique weak solution is proved by means of a fixed-point argument, and by employing maximal parabolic regularity theory. The weak continuity of the solution operator is also shown. As an application, the existence of a global minimizer of a class ...

We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original prob...

We consider a nonlocal isoperimetric problem defined in the whole space RN , whose nonlocal part is given by a Riesz potential with exponent α ∈ (0, N − 1) . We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L1 -norm. This criterion provides the existence of a (explicitly determined) critical thresh...

In this paper, a class of new auxiliary function with one parameter on constrained problem for escaping the current local minimizer of global optimization problem is proposed. Firstly, we give a definition of the quasifilled function for constrained problem and under some mild assumptions, we prove the proposed auxiliary function is a quasi-filled function. Then, a new algorithm is presented ac...

We discuss the Lp (0 ≤ p < 1) minimization problem arising from sparse solution construction and compressed sensing. For any fixed 0 < p < 1, we prove that finding the global minimal value of the problem is strongly NP-Hard, but computing a local minimizer of the problem can be done in polynomial time. We also develop an interior-point potential reduction algorithm with a provable complexity bo...

Bioinformatics applications and pipelines increasingly use k-mer indexes to search for similar sequences. The major problem with k-mer indexes is that they require lots of memory. Sampling is often used to reduce index size and query time. Most applications use one of two major types of sampling: fixed sampling and minimizer sampling. It is well known that fixed sampling will produce a smaller ...

A global convergence theorem for unconstrained minimization algorithms with an eecient line search is derived. The theorem applies to a new version of the conjugate gradient method derived here in terms of minimizing the eeect of zigzagging. The global convergence condition makes much weaker demands on the line search than previous methods. Local Q-linear convergence in a neighborhood of a stro...

In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded number of vortices when the applied magnetic field hex < Hc1 +K log | log ε| where Hc1 is the lower critical field of the film obtained by Ding and Du in SIAM J. Math. Anal., 2002. ...

It is known that any local maximizer of an explicitly quasiconvex realvalued function is actually a global minimizer, whenever it belongs to the intrinsic core of the function’s domain. We show that a similar property holds for componentwise explicitly quasiconvex vector-valued functions, with respect to the optimality concepts of ideal, strong and weak efficiency. These new results are applied...