This is a functional version of the inverse Santaló inequality for unconditional convex bodies due to J. Saint Raymond. The proof involves a general result on increasing functions on $$\\mathbb{R}^{n} \\times \
Reinforcement learning (RL) is a ML approach which describes how intelligent agents take actions in an interactive environment to maximize an expected cumulative reward35. Recent advances in ML have paired the RL mathematical formalism of decision-making with advances in deep learning to train models ...
Dirichlet convolution is often of interest in the context of multiplicative functions (i.e., functions such that f(a)f(b)=f(ab)f(a)f(b)=f(ab) for gcd(a,b)=1gcd(a,b)=1), as the result can be proven to also be a multiplicative function. Moreover, quite often functions of int...
convex objective function. This issue worsens when considering contact, which leads to abrupt, non-smooth kinks in the stress response. Our model, inspired by generative video modelling, is particularly suited to this nonlinear setting and overcomes many of these challenges, although being, from a ...
15.7). In inverse design problems, the methods based on the identification of the inverse function and its solutions are commonly known as backward methods. However, such an approach is seldom possible in many building physics models due to the nature of the physical–mathematical descriptions ...
the user. For instance, if an experimentalist wishes to design materials with a stringent objective of a large bulk modulus but a more forgiving objective of processing temperature, a reward function that places a strong emphasis on maximizing bulk modulus and a weaker emphasis on minimizing ...
These two objects make the definition of an inverse robust optimization problem very general. The merit function can be simply the volume, but can also contain information about the distribution of the uncertain parameter u. The cover space can either consist of sets with a concrete shape, such...
Wong D.W. An adaptive inverse-distance weighting spatial interpolation technique - Lu () Citation Context ...er for convex F �x � . The core idea is to minimize the function F �x � iteratively [19], and Equation (7) can be simply solved by iterative thresholding: �1T i...
Simulation-based optimization of geometry parameters is an inherent and important stage of microwave design process. To ensure reliability, the optimization process is normally carried out using full-wave electromagnetic (EM) simulation tools, which enta
DL can learn highly non-linear functions mapping the inputs to the outputs in a training dataset by using deep artificial neural networks (NNs) with layer architectures that are amenable to training using convex optimization despite their depth. With a sufficient amount of training data and ...