In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

The problem considered is as follows: given C ⊂ R and F : C → R differentiable, find f : C → R differentiable such that ‖∇f(x)‖−1∇f(x) = ‖F (x)‖−1F (x) for all x ∈ C. Conditions for f to be pseudoconvex or convex are given. The results are applied to the differentiable case of the revealed preference problem.

The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...

In this paper, we present a simple, yet effective, attention and memory mechanism that is reminiscent of Memory Networks and we demonstrate it in question-answering scenarios. Our mechanism is based on four simple premises: a) memories can be formed from word sequences by using convolutional networks; b) distance measurements can be taken at a neuronal level; c) a recursive softmax function can...

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

This paper presents a novel solution method for joint energy and Spinning Reserve (SR) dispatch problem. In systems in which the Lost Opportunity Cost (LOC) should be paid to generators, if the LOC is not considered in the dispatch problem, the results may differ from the truly optimum solution. Since the LOC is a non-differentiable function, including it in the formulation makes the problem so...