Diierent optimization methods can be employed to otpimize a numerical estimate for the match between an instantiated object model and an image. In order to take advantage of gradient-based optimization methods, perspective inversion must be used in this context. We show that convergence can be very fast by extrapolating to maximum goodness-of-t with Newton's method. This approach is related to ...

In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network inference. Despite the apparent lack of convexity in such functions, we prove that stochastic projected gradient methods can provide strong approximation gu...

When applied to an unconstrained minimization problem with a convex objective, the steepest descent method has stronger convergence properties than in the noncovex case: the whole sequence converges to an optimal solution under the only hypothesis of existence of minimizers (i.e. without assuming e.g. boundedness of the level sets). In this paper we look at the projected gradient method for con...

A smoothing projected gradient (SPG) method is proposed for the minimization problem on a closed convex set, where the objective function is locally Lipschitz continuous but nonconvex, nondifferentiable. We show that any accumulation point generated by the SPG method is a stationary point associated with the smoothing function used in the method, which is a Clarke stationary point in many appli...

The paper is concerned with linear bilevel problems. These nonconvex problems are known to be NP-complete. So, no efficient method for solving the global bilevel problem can be expected. In this paper we give a genericity analysis of linear bilevel problems and present a new algorithm for computing efficiently local minimizers. The method is based on the given structural analysis and combines i...

In this paper a numerical method based on least-squares approximation is proposed for elliptic interface problems in two dimensions, where the interface is smooth. The underlying method is spectral element method. In the least-squares formulation a functional is minimized as defined in (4.1). The jump in the solution and its normal derivative across the interface are enforced (in an appropriate...

A minimax method for finding multiple critical points in Banach spaces is successfully developed in [12] by using a projected pseudo-gradient as a search direction. Since several different techniques can be used to compute a projected pseudo-gradient, the uniform stepsize and the continuity of a search direction, two key properties for the convergence results in [5], get lost. In this paper, in...