The ramp loss is a robust but non-convex loss for classification. Compared with other non-convex losses, a local minimum of the ramp loss can be effectively found. The effectiveness of local search comes from the piecewise linearity of the ramp loss. Motivated by the fact that the `1-penalty is piecewise linear as well, the `1-penalty is applied for the ramp loss, resulting in a ramp loss linea...

Clifford A. Meyer and Christodoulos A. Floudas Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA Abstract This paper presents an efficient branch and bound approach to address the global optimization of constrained optimization problems with twice differentiable functions. A lower bound on the global minimum is determined via a convex nonlinear programming probl...

In this paper, an integrated machine scheduling withits due date setting problem has been considered. It is assumed that the machine is subject to some kind of random unavailability. Due dates should be set in an attractive and reliable manner, implying that they should be short and possible to be met. To this end, first, long due dates are penalized in the objective function. Then, for each cu...

We consider the problem of minimizing a separable convex objective function over the linear space given by system Mx = 0 with M a totally unimodular matrix. In particular, this generalizes the usual minimum linear cost circulation and co-circulation problems in a network, and the problems of determining the Euclidean distance from a point to the perfect bipartite matching polytope and the feasi...

In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

Partially Observable Markov Decision Processes (POMDPs) model sequential decision-making problems under uncertainty and partial observability. Unfortunately, some problems cannot be modeled with state-dependent reward functions, e.g., problems whose objective explicitly implies reducing the uncertainty on the state. To that end, we introduce ρPOMDPs, an extension of POMDPs where the reward func...

In this paper we present a bundle method for solving a generalized variational inequality problem. This problem consists in nding a zero of the sum of two multivalued operators de ned on a real Hilbert space. The rst one is monotone and the second one is the subdi erential of a lower semicontinuous proper convex function. The method is based on the auxiliary problem principle due to Cohen and t...

In this paper a model of oil depletion is analyzed in which the shapes of field profiles are triangular and the sizes of successive fields decrease monotonically. It is shown that the curve representing the rate of production for this model is piecewise linear and concave up to a certain point after which it is monotone decreasing. Equations for natural smooth approximating curves having unique...