We study N = 1 global and local supersymmetric theories with a continuous global U(1)R symmetry. We discuss conditions for supersymmetry (SUSY) breaking and vacuum structures of R-symmetric SUSY models. Especially we find the conditions for R-symmetry breaking and runway vacua in global supersymmetric theories. We introduce explicit R-symmetry breaking terms into such models in global and local...

In this article, we construct a Fenchel-Lagrangian ε-dual problem for set-valued optimization problems by using the perturbation methods. Some relationships between the solutions of the primal and the dual problems are discussed. Moreover, an ε-saddle point theorem is proved.

We study N = 1 global and local supersymmetric theories with a continuous global U(1)R symmetry. We discuss conditions for supersymmetry (SUSY) breaking and vacuum structures of R-symmetric SUSY models. Especially we find the conditions for R-symmetry breaking and runway vacua in global supersymmetric theories. We introduce explicit R-symmetry breaking terms into such models in global and local...

A weakness of classical methods for solving Markov decision processes is that they scale very poorly because of the flat state space, which subjects them to the curse of dimensionality. Fortunately, many MDPs are well-structured, which makes it possible to avoid enumerating the state space. To this end, factored MDP representations have been proposed (Boutilier, Dearden, & Goldszmidt 1995; Koll...

In this paper, we prove the convergence of a discrete duality finite volume scheme for a system of partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration. We first establish some a priori estimates satisfied...

The perceptron and the von Neumann algorithms were developed to solve Linear Feasibility Problems. In this paper, we investigate and reveal the duality relationship between these two algorithms. The specific forms of Linear Feasibility Problems solved by the perceptron and the von Neumann algorithms are a pair of alternative systems by the Farkas Lemma. A solution of one problem serves as an in...

Throughout, X stands for a real Banach space, SX for its unit sphere, X ∗ for its topological dual, and 〈·, ·〉 for the duality pairing. All the functions f : X → R∪{+∞} are lower semicontinuous. The Clarke subdifferential , the Hadamard subdifferential and the Fréchet subdifferential of f are respectively denoted by ∂Cf , ∂Hf and ∂F f . The Zagrodny two points mean value inequality has proved t...

Abstract: We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. Th...

Minimax Weighted Constraint Satisfaction Problems (formerly called QWCSPs) are a framework for modeling soft constrained problems with adversarial conditions. In this paper, we describe novel definitions and implementations of node, arc and full directional arc consistency notions to help reduce search space on top of the basic tree search with alpha-beta pruning for solving ultraweak solutions...

The ltering problem for discrete Volterra equations is a nontrivial task due to an increasing dimension of the equivalent single step process model A di erence equation of a moderate dimension is chosen as an approximate model for the original system Then the reduced Kalman lter can be used as an approximate but e cient estimator Using the duality theory of convex variational problems a level o...