Sentence examples for inner approximation from inspiring English sources

By adopting the inner approximation method (see, e.g., [30]), our strategy is to iteratively approximate function F by a concave function F that possesses the following two crucial properties: It matches the nonconcave objective function F at (x,y, i.e., begin{array}{*{20}l} F^{ kappa)}left(x^{ kappa }, y^{ kappa)}right) &= Fleft(x^{ kappa }, y^{ kappa)}right).

The boundary condition at the origin has been taking into account using an inner approximation for a boundary layer.

In particular, the original problem is converted into successive convex programs by using an inner approximation method such that each iteration involves only a simple convex quadratic program.

Then, for a given fixed horizon length and block count determined by hardware capabilities, the second problem seeks to maximise the volume of an inner approximation to the region of attraction.

Iteration step: Inner approximation (additive Schwarz algorithm with two subdomains).

2. Iteration step:   (a) Inner approximation (additive Schwarz algorithm with two subdomains).

The novelty of the proposed approach relies upon the capability to combine sequences of inner approximations of one-step controllable sets with polyhedral piecewise state-space partitions.

As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of size m) of the nonconvex set of Schur stable polynomials of given degree n<m.

Actually, this gives inner approximations for the coincidence set N 0. There are many algorithms based on active set strategy.

In order to find the largest possible estimates of the DA's of x e 1 and x e 2, namely D ~ 1 and D ~ 2, our procedure takes two small initial polytopic regions, surrounding the equilibrium points, and then iteratively stretches them along the different dimensions of the state space until the feasibility conditions are no longer verified, thus obtaining two inner approximations of the DA's.

First, a set of stabilizing LPV controllers is given as an inner convex approximation of the non-convex set of all stabilizing LPV controllers with the same order.