Min–max problems have broad applications in machine learning, including learning with non-decomposable loss and robustness to data distribution. Convex–concave min–max problem is an active topic of research efficient algorithms sound theoretical foundations developed. However, it remains a challenge design provably for non-convex or without smoothness. In this paper, we study family problems, w...

An inequality g{x) 2i 0 is often said to be a reverse convex constraint if the function g is continuous and convex. The feasible regions for linear program with an additional reverse convex constraint are generally non-convex and disconnected. In this paper a convergent algorithm for solving such a linear problem is proposed. The method is based upon a combination of the branch and bound proced...

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel problem, where the lower-level problem is convex equality inequality constraints upper-level non-convex. The overall objective function non-convex non-differentiable. To solve we develop gradient-based approach, called gradient approximat...

in order to have better insight of project characteristics, different kinds of fuzzy analysis for project networks have been recently proposed, most of which consider activities duration as the main and only source of imprecision and vagueness, but as it is usually experienced in real projects, the structure of the network is also subject to changes. in this paper we consider three types of imp...

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective function downhill. Such a simple principle is widely applicable and has been very popular in various scientific fields, especially in signal processing and statist...

Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a mixed integer program (MIP) whose objective function is non-convex. In this form, the problem is resistant to standard optimization techniques. We construct MIP...