We present a vectorial self dual morphological filter. Contrary tomanymethods, our approach does not require the use of an ordering on vectors. It relies on theminimization of the total variationwithL norm as data fidelity on each channel. We further constraint this minimization in order not to create new values. It is shown that this minimization yields a self-dual and contrast invariant filte...

A normal quartic polynomial is a quartic polynomial whose fourth degree term coefficient tensor is positive definite. Its minimization problem is one of the simplest cases of nonconvex global optimization, and has engineering applications. We call a direction a global descent direction of a function at a point if there is another point with a lower function value along this direction. For a nor...

This paper proposes modeling motion in a bilateral domain that augments spatial information with the motion itself. We use the bilateral domain to reformulate a piecewise smooth constraint as continuous global modeling constraint. The resultant model can be robustly computed from highly noisy scattered feature points using a global minimization. We demonstrate how the model can reliably obtain ...

The nonlinear conjugate gradient method is a very useful technique for solving large scale minimization problems and has wide applications in many fields. In this paper, we present a new algorithm of nonlinear conjugate gradient method with strong convergence for unconstrained minimization problems. The new algorithm can generate an adequate trust region radius automatically at each iteration a...

Abstract. Regularized minimization problems with nonconvex, nonsmooth, perhaps nonLipschitz penalty functions have attracted considerable attention in recent years, owing to their wide applications in image restoration, signal reconstruction and variable selection. In this paper, we derive affine-scaled second order necessary and sufficient conditions for local minimizers of such minimization p...

Canonical duality theory is a potentially powerful methodology, which can be used to solve a wide class of discrete and continuous global optimization problems. This paper presents a brief review and recent developments of this theory with applications to some well-know problems including polynomial minimization, mixed integer and fractional programming, nonconvex minimization with nonconvex qu...

Heterogeneous network protocol systems are integrated together to fulfill complex tasks and their interoperability is a major hurdle for the network reliability and quality of services. We identify a new equivalence relation of states that preserves the integrated system interface behaviors. Based on this state equivalence we study the minimization of the system components with respect to their...

The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathematical programming. In addition to providing a unified framework for bilevel and inverse linear optimization, nonconvex piecewise linear programming, indefinite quadratic programs, ...

We study a Newton-like method for the minimization of an objective function φ that is the sum of a smooth convex function and an `1 regularization term. This method, which is sometimes referred to in the literature as a proximal Newton method, computes a step by minimizing a piecewise quadratic model qk of the objective function φ. In order to make this approach efficient in practice, it is imp...

Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated...