driven by white noise Ẇ . Under minimal assumptions on regularity of the coefficients and random forces, the existence of a global weak (martingale) solution of the stochastic Navier–Stokes equation is proved. In the two-dimensional case, the existence and pathwise uniqueness of a global strong solution is shown. A Wiener chaosbased criterion for the existence and uniqueness of a strong global ...

This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, there lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. This equivalence facili...

In this paper, we study the semilinear pseudo-parabolic equations ut − 4Bu − 4But = |u|p−1 u on a manifold with conical singularity, where 4B is Fuchsian type Laplace operator investigated with totally characteristic degeneracy on the boundary x1 = 0. Firstly, we discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we deri...

We propose a method for finding a global optimal solution of programs with linear complementarity constraints. The program arises for instance from the bilevel programs. The main idea of the method is to generate a sequence of points either ending at a global optimal solution within a finite number of iterations or converging to a global optimal solution. The construction of such a sequence is ...

We propose a method for finding a global optimal solution of programs with linear complementarity constraints. The program arises for instance from the bilevel programs. The main idea of the method is to generate a sequence of points either ending at a global optimal solution within a finite number of iterations or converging to a global optimal solution. The construction of such a sequence is ...

Given non-empty subsets A and B of a metric space, let S : A → B and T : A → B be non-self mappings. Taking into account the fact that, given any element x in A, the distance between x and Sx, and the distance between x and Tx are at least d(A,B), a common best proximity point theorem affirms global minimum of both functions x → d(x, Sx) and x → d(x, Tx) by imposing a common approximate solutio...

There is a lack of a representative set of test problems for comparing global optimization methods. To remedy this a classiication of essentially un-constrained global optimization problems into unimodal, easy, moderately diicult, and diicult problems is proposed. The problem features giving this classiication are the chance to miss the basin of the global minimum, the dispersion of minima, and...

Recent results on the solution of large, banded or sparse systems and on global unconstrained optimization problems including verification of the correctness of the result will be discussed. The computing time for the verification for large linear systems is the same as for the decomposition, the total computational effort for verifying the global optimum value is for well-known test examples c...

The problem of global solution of Fredholm integral equations is studied. This means that one seeks to approximate the full solution function (as opposed to the local problem, where only the value of the solution in a single point or a functional of the solution is sought). The Monte Carlo complexity is analyzed, i. e. the complexity of stochastic solution of this problem. The framework for thi...

Solvers for Quantified Boolean Formulae (QBF) use many analogues of technique from SAT. A significant amount of work has gone into extending conflict based techniques such as conflict learning to solution learning, which is irrelevant in SAT but can play a large role in success in QBF. Unfortunately, solution learning techniques have not been highly successful to date. We argue that one reason ...