Steepest descent is central in variational mathematics. We present a new transparent existence proof for curves of near-maximal slope — an influential notion of steepest descent in a nonsmooth setting. We moreover show that for semi-algebraic functions — prototypical nonpathological functions in nonsmooth optimization — such curves are precisely the solutions of subgradient dynamical systems.

Taking hybrid biomass sawdust as the material, carry out simulation calibration experiment with JKR contact model based on DEM principle. The Plackett-Burman factorial is carried by Design-Expert for 10 related factors. Combined steepest climbing test scheme, according to Box-Behnken experiment, parameter of multi-response Indicators completed. results are follows: Poisson's ratio 0.30, density...

This paper proposes a real-life volume reduction for cancer cells using optimal doses of radiation and an anti-angiogenic drug. A generalized dynamical system based on the diffusion-consumption equation along with stimulation inhibition factors is proposed. To achieve continuous low-dose therapy, related problem simulated by regulator mathematically. By combining steepest descent, conjugate gra...

This paper addresses the minimal subset selection of antennas achieving designated channel capacity. This is one of the most natural approaches to alleviating the power consumption in MIMO systems, while it is a mathematically challenging nonlinearlyconstrained sparse optimization ( -norm minimization) problem. We present an ef cient algorithmic solution, to this highly combinatorial problem, u...

Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This chapter investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework o...

Tree detection and reconstruction is of great interest in large-scale city modelling. In this paper, we present a marked point process model to detect single trees from airborne laser scanning (ALS) data. We consider single trees in ALS recovered canopy height model (CHM) as a realization of point process of circles. Unlike traditional marked point process, we sample the model in a constraint c...