First-order Takagi-Sugeno models are mainly based on the interpolation between several local affine functions usually defined on trapezoidal fuzzy partitions. The standard computational model presents some shapefailures: the approximation does not preserve the positivity, monotony or convexity of the data that belong to the corresponding antecedent term cores. Moreover the standard output does ...

In this technical report we treat some properties of the recently introduced QBGvalue function. In particular we show that it is a piecewise linear and convex function over the space of joint beliefs. Furthermore, we show that there exists an optimal infinite-horizon QBG-value function, as the QBG backup operator is a contraction mapping. We conclude by noting that the optimal Dec-POMDP Q-value...

The present paper introduces a procedure to recover an inverse parametric linear or quadratic programming problem from a given polyhedral partition over which a continuous piecewise affine function is defined. The solution to the resulting parametric linear problem is exactly the initial piecewise affine function over the given original parameter space partition. We provide sufficient condition...

To facilitate the damping matching of dampers for vehicle passive suspensions, this paper proposes an analytical matching method of the optimal piecewise linear damping characteristics curve. Based on the vehicle vibration model, taking the suspension dynamic deflection as the constraint, by the vibration acceleration and the wheel dynamic load, an objective function about the relative damping ...

We provide a general framework to construct finite-dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give precise estimates of the distance between the approximation space and the admissible set. This framework applies to the approximation of convex functions by piecewise-...

Let Ω be a convex domain with smooth boundary in Rd. It has been shown recently that the semigroup generated by the discrete Laplacian for quasi-uniform families of piecewise linear finite element spaces on Ω is analytic with respect to the maximum-norm, uniformly in the mesh-width. This implies a resolvent estimate of standard form in the maximum-norm outside some sector in the right halfplane...

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...

ABSTRACT We describe efficient interior-point methods for the design of filters with constraints on the magnitude spectrum, for example, piecewise-constant upper and lower bounds, and arbitrary phase. Several researchers have observed that problems of this type can be solved via convex optimization and spectral factorization. The associated optimization problems are usually solved via linear pr...