In this paper, we establish global optimality conditions for quadratic optimization problems with quadratic equality and bivalent constraints. We first present a necessary and sufficient condition for a global minimizer of quadratic optimization problems with quadratic equality and bivalent constraints. Then, we examine situations where this optimality condition is equivalent to checking the po...

This work presents a filled function method based on the filter technique for global optimization. Filled function method is one of the effectivemethods for nonlinear global optimization, since it can effectively find a better minimizer. Filter technique is applied to local optimization methods for its excellent numerical results. In order to optimize the filled function method, the filter meth...

A novel algorithm for the global optimization of functions (C-RTS) is presented, in which a combinato-rial optimization method cooperates with a stochastic local minimizer. The combinatorial optimization component, based on the Reactive Tabu Search recently proposed by the authors, locates the most promising \boxes," where starting points for the local minimizer are generated. In order to cover...

We propose a Bayesian approach for recursively estimating the classifier weights in online learning of a classifier ensemble. In contrast with past methods, such as stochastic gradient descent or online boosting, our approach estimates the weights by recursively updating its posterior distribution. For a specified class of loss functions, we show that it is possible to formulate a suitably defi...

We shall be concerned with the construction of Tikhonov–based iteration schemes for solving nonlinear operator equations. In particular, we are interested in algorithms for the computation of a minimizer of the Tikhonov functional. To this end, we introduce a replacement functional, that has much better properties than the classical Tikhonov functional with nonlinear operator. Namely, the repla...

|f(x,A)| ≤ c(1 + |A|), for some c > 0 and 1 ≤ p < ∞, and u lies in the Sobolev space of vector-valued functions W 1,p(Ω,Rm). We study the implications of a function u0 being a critical point of F . In this regard we show among other things that if f does not depend on the spatial variable x, then every piecewise affine critical point of F is a global minimizer subject to its own boundary condit...

An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for unconstrained optimization, generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981, DAMTP, Univ. of Cambridge), an algorithm by Nesterov & Polyak (Math. Programming 108(1), 2006, pp 177-205) and a proposal by Weiser, Deuflhard & Erdmann (Optim. Methods Softw. 22(3), 2007, pp 413-43...

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations usefully contributes to the localization of good candidates for the role of global minimizer, a stochastic model of the function can be built to conduct a sequential choice of evaluation points. Based on Gaus...

In this paper, we consider the problem of recovering a sparse vector from noisy measurement data. Traditionally, it is formulated as a penalized least-squares problem with an `1 penalty. Recent studies show that nonconvex penalties, e.g., `0 and bridge, allow more effective sparse recovery. We develop an algorithm of primal dual active set type for a class of nonconvex sparsity-promoting penalt...