We are concerned in this paper with the general problem of finding an unrestricted local minimum of a function J[xu x2 • • •, xn) of several variables xx, x2, • •., xn. We suppose that the function of interest can be calculated at all points. It is convenient to group functions into two main classes according to whether the gradient vector g, = Wbx, is defined analytically at each point or must...

In this paper, we propose and analyse an approximate variant of the level method of Lemaréchal, Nemirovskii and Nesterov for minimizing nonsmooth convex functions. The main per-iteration work of the level method is spent on (i) minimizing a piecewise-linear model of the objective function and (ii) projecting onto the intersection of the feasible region and a level set of the model function. We ...

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh [5] to solving nonsmooth and strongly convex composite problems. We prove that the resulting algorithm, GeoPG, converges with a linear rate (1− 1/√κ), thus achieves the optimal rate among first-order methods, where κ is the condition number of the problem. Numerical results on linear regression and ...

The article describes a new Boolean minimization and single-level partitioning method based on the BOOM minimizer. The minimization is performed with respect to various restrictions stated for the use of input variables. This enables us to effectively decompose the circuit into several components for which the numbers of inputs and outputs are explicitly specified. The method can thus be used t...

We present an efficient preconditioner for the orbital minimization method when the Hamiltonian is discretized using planewaves (i.e., pseudospectral method). This novel preconditioner is based on an approximate Fermi operator projection by pole expansion, combined with the sparsifying preconditioner to efficiently evaluate the pole expansion for a wide range of Hamiltonian operators. Numerical...

In this paper we propose an inexact proximal point method to solve constrained minimization problems with locally Lipschitz quasiconvex objective functions. Assuming that the function is also bounded from below, lower semicontinuous and using proximal distances, we show that the sequence generated for the method converges to a stationary point of the problem.