Abstract In this paper, we introduce a new concept of sets and class functions called $$\alpha$$ α - E -invex V-E-preinvex functions. Furthermore, generalized convexity is introduced for (not necessarily) differentiable vector optimization problems. Namely, the V -type I defined -differentiable problem. A num...

1. Terminology. V and M will be differentiable manifolds of dimension n and m respectively; differentiable meaning always of class C. For simplicity, we assume V compact and without boundary. We shall have to consider several categories of maps: (1) the category of continuous maps, (2) the category of topological imbeddings, (3) the category of topological immersions: a map ƒ: F—>M is a topolog...

We describe a new spatio-temporal video autoencoder, based on a classic spatial image autoencoder and a novel nested temporal autoencoder. The temporal encoder is represented by a differentiable visual memory composed of convolutional long short-term memory (LSTM) cells that integrate changes over time. Here we target motion changes and use as temporal decoder a robust optical flow prediction m...

Given f: Rn+ ~ R n, the complementarity problem is to find a solution to x > O, f(x) >_ 0, and (x, f(x)) = 0. Under the condition that fis continuously differentiable, we prove that for a generic set of such an f, the problem has a discrete solution set. Also, under a set of generic non-degeneracy conditions and a condition that implies existence, we prove that the problem has an odd number of ...

This paper presents an extensible framework for designing analog filters that exhibit several desired behavioral properties after being realized in circuits. In the framework, we model the constrained nonlinear optimization problem as a sequential quadratic programming (SQP) problem. SQP requires real-valued constraints and objective functions that are differentiable with respect to the free pa...

By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, th...

The article is concerned with the derivation of a posteriori error estimates for optimization problems subject to an obstacle problem. To circumvent the nondifferentiability inherent to this type of problem, we introduce a sequence of penalized but differentiable problem. We show differentiability of the central path and derive separate a posteriori dual weighted residual estimates for the erro...

Generative adversarial learning is a popular new approach to training generative models which has been proven successful for other related problems as well. The general idea is to maintain an oracle D that discriminates between the expert’s data distribution and that of the generative model G. The generative model is trained to capture the expert’s distribution by maximizing the probability of ...

Two functional equations are considered that are motivated by three considerations: work in utility theory and psychophysics, questions concerning when pairs of degree 1 homogeneous functions can be homomorphic and calculating their homomorphisms, and the link of the latter questions to quasilinear mean values. The first equation is h(σ(y)x + [1 - σ(y)]y) = τ(y)h(x) + [1 - τ(y)]h(y) (x ≥ y ≥ 0)...