— In this paper, the performances of the quasi-Newton BFGS algorithm, the NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm Optimizers (PSO) are compared experimentally on benchmark functions reflecting important challenges encountered in real-world optimization problems. Dependence of the...

We study the problem of learning a kernel matrix from an apriori kernel and training data. An unconstrained convex optimization formulation is proposed, with an arbitrary convex smooth loss function on kernel entries and a LogDet divergence for regularization. Since the number of variables is of order O(n), standard Newton and quasi-Newton methods are too time-consuming. An operator form Hessia...

A physics-based multicell electrothermal equivalent circuit model is described that is applied to the large-signal microwave characterization of AlGaAs/GaAs HBT’s. This highly efficient model, which incorporates a new multifinger electrothermal model, has been used to perform dc, small-signal and loadpull characterization, and investigate parameter-spreads due to fabrication process variations....

Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient but also very reliable. Unfortun...

In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as paramete...

A Hessian matrix in full waveform inversion (FWI) is difficult to compute directly because of high computational cost and an especially large memory requirement. Therefore, Newton-like methods are rarely feasible in realistic large-size FWI problems. We modify the quasi-Newton BFGS method to use a projected Hessian matrix that reduces both the computational cost and memory required, thereby mak...

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for the ability of these local methods to find the global minimum is the proliferation o...

We develop a theory of quasi-Newton and least-change update methods for solving systems of nonlinear equations F (x) = 0. In this theory, no diierentiability conditions are necessary. Instead, we assume that F can be approximated, in a weak sense, by an aane function in a neighborhood of a solution. Using this assumption, we prove local and ideal convergence. Our theory can be applied to B-diie...

We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We presen...

A physics-based multi-cell electro-thermal equivalent circuit model is described which is applied to the large-signal microwave characterization of AlGaAs/GaAs HBTs. This highly efficient model, which incorporates a new multi-finger electro-thermal model, has been used to perform DC, small-signal and load-pull characterization and investigate parameter-spreads due to fabrication process variati...