A Full-Newton Step Interior Point Method for Fractional Programming Problem Involving Second Order Cone Constraint

Some efficient interior-point methods (IPMs) are based on using a self-concordant barrier function related to the feasibility set of the underlying problem.Here, we use IPMs for solving fractional programming problems involving second order cone constraints. We propose a logarithmic barrier function to show the self concordant property and present an algorithm to compute $\varepsilon-$solution of a fractional programming problem. Finally, we provide a numerical example to illustrate the approach.

Optimal grasp force for robotic grasping and in-hand manipulation with impedance control

Purpose The purpose of this paper is to achieve stable grasping and dexterous in-hand manipulation, the control of the multi-fingered robotic hand is a difficult problem as the hand has many degrees of freedom with various grasp configurations. Design/methodology/approach To achieve this goal, a novel object-level impedance control framework with optimized grasp force and grasp quality is proposed for multi-fingered robotic hand grasping and in-hand manipulation. The minimal grasp force optimization aims to achieve stable grasping satisfying friction cone constraint while keeping appropriate contact forces without damage to the object. With the optimized grasp quality function, optimal grasp quality can be obtained by dynamically sliding on the object from initial grasp configuration to final grasp configuration. By the proposed controller, the in-hand manipulation of the grasped object can be achieved with compliance to the environment force. The control performance of the closed-loop robotic system is guaranteed by appropriately choosing the design parameters as proved by a Lyapunove function. Findings Simulations are conducted to validate the efficiency and performance of the proposed controller with a three-fingered robotic hand. Originality/value This paper presents a method for robotic optimal grasping and in-hand manipulation with a compliant controller. It may inspire other related researchers and has great potential for practical usage in a widespread of robot applications.

On approximate solutions for convex semi-infinite programming with uncertainty

In this paper, we consider approximate solutions (also called $\varepsilon$-solutions) for semi-infinite optimization problems that objective function and constraint functions with uncertainty data are all convex, and establish robust counterpart of convex semi-infinite program and then consider approximate solutions for its. Moreover, the robust necessary condition and robust sufficient theorems are obtained. Then the duality results of the Lagrangian dual approximate solution is given by the robust optimization approach under a cone constraint qualification.

SEQUENTIAL LAGRANGE MULTIPLIER CONDITIONS FOR MINIMAX PROGRAMMING PROBLEMS

In this article, we study nonsmooth convex minimax programming problems with cone constraint and abstract constraint. Our aim is to develop sequential Lagrange multiplier rules for this class of problems in the absence of any constraint qualification. These rules are obtained in terms of ∊-subdifferentials of the functions. As an application of these rules, a sequential dual is proposed and sequential duality results are presented.