Let V be a finite configuration of voter ideal points in the Euclidean plane. For given > 0 a point x ∈ < is in the -core if for all y 6= x, ||v−x|| ≤ ||v− y||+ for a simple majority (at least |V |/2) of voters v ∈ V . Let (x) denote the the least for which x is in the -core. Thus (x) = 0 if and only if x is a core point. The least for which the -core is nonempty is denoted ∗. This paper provid...

In this paper the results in [S. Leyendecker, P. Betsch, P. Steinmann, Energy-conserving integration of constrained Hamiltonian systems—a comparison of approaches, Comput. Mech. 33 (2004) 174–185] are extended to geometrically exact beams. The finite element formulation for nonlinear beams in terms of directors, providing a framework for the objective description of their dynamics, is considere...

Penalization procedures often suffer from their dependence on multiplying factors, whose optimal values are either unknown or hard to estimate from the data. We propose a completely data-driven calibration algorithm for this parameter in the least squares regression framework, without assuming a particular shape for the penalty. Our algorithm relies on the concept of minimal penalty, recently i...

We study a nonlinear exact penalization for optimization problems with a single constraint. The penalty function is constructed as a convolution of the objective function and the constraint by means of IPH (increasing positively homogeneous) functions. The main results are obtained for penalization by strictly IPH functions. We show that some restrictive assumptions, which have been made in ear...

In this paper we study firstand second-order necessary conditions for nonlinear programming problems from the viewpoint of exact penalty functions. By applying the variational description of regular subgradients, we first establish necessary and sufficient conditions for a penalty term to be of KKT-type by using the regular subdifferential of the penalty term. In terms of the kernel of the subd...

To formulate a single-leg seat inventory control problem in an airline ticket sales system, the concept and techniques of revenue management are applied in this research. In this model, it is assumed the cabin capacity is stochastic and hence its exact size cannot be forecasted in advance, at the time of planning. There are two groups of early-reserving and late-purchasing customers demanding t...

In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a...

An iteration of the stabilized sequential quadratic programming method (sSQP) consists in solving a certain quadratic program in the primal-dual space, regularized in the dual variables. The advantage with respect to the classical sequential quadratic programming (SQP) is that no constraint qualifications are required for fast local convergence (i.e., the problem can be degenerate). In particul...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

We deal with the problem of planning collisionfree trajectories for robots operating in a shared space. Given the start and destination position for each of the robots, the task is to find trajectories for all robots that reach their destinations with minimum total cost such that the robots will not collide when following the found trajectories. Our approach starts from individually optimal tra...