x f(x, θ) log f(x, θ) exists for all θ and θ. In principle, one can apply the sum-product algorithm in order to find (1), which involves the following two steps [2]: 1. Determine f(θ) by sum-product message passing. 2. Maximization step: compute θmax △ = argmaxθ f(θ). This procedure is often not feasible, since • When the variable x is continuous, the sum-product rule may lead to intractable in...

This paper presents a descent direction method for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we define a set-valued mapping x → ∂εf(x) named ε-subdifferential which is an approximation for the Clarke subdifferential and which generalizes the Goldstein-ε-subdifferential to the Riemannian setting. Using this notion we construct a steepest descent ...

Comparative study among Least Square Method: LSM, Steepest Descent Method: SDM, and Conjugate Gradient Method: CGM for atmospheric sounder data analysis (estimation of vertical profiles for water vapor) is conducted. Through simulation studies, it is found that CGM shows the best estimation accuracy followed by SDM and LSM. Method dependency on atmospheric models is also clarified. Keywords—non...

This paper is concerned with tracking control of nonlinear multivariable systems whose relative degree is more than one. The control method is based on a direct steepest descent method using the gradient of a performance index. Simulation results demonstrate the usefulness of the proposed method.

We propose here a fully Spice-oriented design algorithm of op-amps for attaining the maximum gains under low power consumptions and assigned slew-rates. Our optimization algorithm is based on a well-known steepest descent method combining with nonlinear programming. The algorithm is realized by equivalent RC circuits with ABMs (analog behavior models) of Spice. The gradient direction is decided...