This paper deals with the adaptation to fuzzy goal programming of the most used methods to formulate, as a linear programming problem, a classic goal programming problem with piecewise linear penalty functions. Up to now, the literature has been only dealing with the adaptation of the Charnes and Cooper’s method. In this paper we show that the mentioned adaptations are not completely correct. W...

This paper studies open-loop stabilization problem for bimodal systems with continuous vector field. It is based on the earlier work of the authors on the controllability problem for the same class of systems. A full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions. It is also shown that controllability implies stabilizability for th...

This article first introduces an extension of the classical cumulative constraint: each task is no more a rectangle but rather a sequence of contiguous trapezoid sub-tasks with variable duration and heights. The resource function is no more constant but is a positive or negative piecewise linear function of time. Finally, a task is no more pre-assigned to one resource, but to a task corresponds...

Electronic exchanges are double-sided marketplaces that allow multiple buyers to trade with multiple sellers, with aggregation of demand and supply across the bids to maximize the revenue in the market. Two important issues in the design of exchanges are (1) trade determination (determining the number of goods traded between any buyerseller pair) and (2) pricing. In this paper we address the tr...

By providing a counterexample we show that there exists a shift-invariant space S generated by a piecewise linear function such that the union of the corresponding scaled spaces Sh (h > 0) is dense in C0(R) but S does not contain a stable and locally supported partition of unity. This settles a question raised by C. de Boor and R. DeVore a decade ago.

We investigate the properties of local minima energy landscape a continuous non-convex optimization problem, spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable displaying set pseudogaps, singularities non-linear excitations whose appear to be in same universality class jammed packings hard spheres. The problem appears as an evolution pure...

The solution path of the 1D fused lasso for an ndimensional input is piecewise linear with O(n) segments [1], [2]. However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the weighted fused lasso is a special case, allow Ω(3) segments [3]. In this paper, we prove that the number of segments in the solution pa...

For each piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a β-transformation.

In this paper, we establish the equivalence between the half-space representation and the vertex representation of a smooth parametric semiclosed polyhedron. By virtue of the smooth representation result, we prove that the solution set of a smooth parametric piecewise linear program can be locally represented as a finite union of parametric semiclosed polyhedra generated by finite smooth functi...