arXiv subjects

Pham Dinh Tao

Publications and source records attributed to Pham Dinh Tao.

3 recordsLinked to original sources

arXiv2026

Object Pose from 2-D to 3-D Point and Line Correspondences

In this paper we present a method for optimally estimating the rotation and translation between a camera and a 3-D object from point and/or line correspondences. First we devise an error function and second we show how to minimize this error function. The quadratic nature of this function is made possible by representing rotation and translation with a dual number quaternion. We provide a detailed account of the computational aspects of a trust-region optimization method. This method compares favourably with Newton's method which has extensively been used to solve the problem at hand, with Faugeras-Toscani linear method [6] for calibrating a camera, and with the Levenberg-Marquardt non-linear optimization method. Finally we present some experimental results which demonstrate the robustness of our method with respect to image noise and matching errors.

cs.CV↗

arXiv2020

Stochastic Difference-of-Convex Algorithms for Solving nonconvex optimization problems

The paper deals with stochastic difference-of-convex functions (DC) programs, that is, optimization problems whose the cost function is a sum of a lower semicontinuous DC function and the expectation of a stochastic DC function with respect to a probability distribution. This class of nonsmooth and nonconvex stochastic optimization problems plays a central role in many practical applications. Although there are many contributions in the context of convex and/or smooth stochastic optimization, algorithms dealing with nonconvex and nonsmooth programs remain rare. In deterministic optimization literature, the DC Algorithm (DCA) is recognized to be one of the few algorithms to solve effectively nonconvex and nonsmooth optimization problems. The main purpose of this paper is to present some new stochastic DCAs for solving stochastic DC programs. The convergence analysis of the proposed algorithms is carefully studied, and numerical experiments are conducted to justify the algorithms' behaviors.

math.NA↗

arXiv2011

Decomposition algorithms for globally solving mathematical programs with affine equilibrium constraints

A mathematical programming problem with affine equilibrium constraints (AMPEC) is a bilevel programming problem where the lower one is a parametric affine variational inequality. We formulate some classes of bilevel programming in forms of MPEC. Then we use a regularization technique to formulate the resulting problem as a mathematical program with an additional constraint defined by the difference of two convex functions (DC function). A main feature of this DC decomposition is that the second component depends upon only the parameter in the lower problem. This property allows us to develop branch-and-bound algorithms for globally solving AMPEC where the adaptive rectangular bisection takes place only in the space of the parameter. As an example, we use the proposed algorithm to solve a bilevel Nash-Cournot equilibrium market model. Computational results show the efficiency of the proposed algorithm.

math.OC↗