Linear Second-order Cone Programming Research Articles

Exploring constraint qualification-free optimality conditions for linear second-order cone programming

Exploring constraint qualification-free optimality conditions for linear second-order cone programming

A new projection neural network for linear and convex quadratic second-order cone programming

A new projection neural network approach is presented for the linear and convex quadratic second-order cone programming. In the method, the optimal conditions of the linear and convex second-order cone programming are equivalent to the cone projection equations. A Lyapunov function is given based on the G-norm distance function. Based on the cone projection function, the descent direction of Lyapunov function is used to design the new projection neural network. For the proposed neural network, we give the Lyapunov stability analysis and prove the global convergence. Finally, some numerical examples and two kinds of grasping force optimization problems are used to test the efficiency of the proposed neural network. The simulation results show that the proposed neural network is efficient for solving some linear and convex quadratic second-order cone programming problems. Especially, the proposed neural network can overcome the oscillating trajectory of the exist projection neural network for some linear second-order cone programming examples and the min-max grasping force optimization problem.

A Line Search Penalty-Free Method for Nonlinear Second-Order Cone Programming

In this paper, we propose a line search penalty-free method for solving nonlinear second-order cone programming (NSOCP) problem. Compared with the traditional SQP-type method for NSOCP, our method does not need the assumption that the subproblem is feasible. Besides that, it does not use penalty-function or filter technique. We first use a robust linear second-order cone programming subproblem to get a detective step and then compute an optimal step from a quadratic optimization subproblem. The search direction is a convex combination of the detective step and optimal step. This two-phase strategy and the penalty-free technique are employed to promote global convergence which is analyzed under mild assumptions. We report some numerical experiments whose results show that the proposed algorithm is applicable and efficient.

Analysis of smoothing-type algorithms for the convex second-order cone programming

There recently has been much interest in smoothing-type algorithms for solving the linear second-order cone programming (LSOCP). We extend such method to solve the convex second-order cone programming (CSOCP), which is an extension of the LSOCP. In this paper, we first propose a new smoothing function. Based on this function, we establish a smoothing Newton algorithm for solving the CSOCP and prove that the algorithm is globally and locally quadratically convergent under suitable assumptions. For the established algorithm, we use a generalized Armijo-type search rule to generate the step size. Some numerical results are reported which indicate the effectiveness of our algorithm.

A majorized penalty approach to inverse linear second order cone programming problems

This paper focuses on a type of inverse linear second order cone programming (LSOCP) problems which require us to adjust the parameters in both the objective function and the constraint set of a given LSOCP problem as little as possible so that a known feasible solution becomes optimal one. This inverse problem can be formulated as a linear second order cone complementarity constrained optimization problem and is difficult to solve due to the presence of second order cone complementarity constraint. To solve this difficult problem, we first partially penalize the inverse problem and then propose the majorization approach to the penalized problem by solving a sequence of convex optimization problems with quadratic objective function and simple second order cone constraints. Numerical results demonstrate the efficiency of our approach to inverse LSOCP problems.

A class of Smoothing Method for Linear Second-Order Cone Programming

A class of Smoothing Method for Linear Second-Order Cone Programming

A perturbation approach for an inverse linear second-order cone programming

A type of inverse linear second-order cone programming problems is discussed, in which the parameters in both the objective function and the constraint set of a given linear second-order cone programming need to be adjusted as little as possible so that a known feasible solution becomes optimal. This inverse problem can be formulated as a minimization problem with second-order cone complementarity constraints. With the help of the smoothed Fischer-Burmeister function over second-order cones, we construct a smoothing approximation of the formulated problem whose feasible set and optimal solution set are demonstrated to be continuous and outer semicontinuous respectively at the perturbed parameter $\varepsilon=0$. A damped Newton method is employed to solve the perturbed problem and its global convergence and local quadratic convergence rate are shown. Finally, the numerical results are reported to show the effectiveness of the damped Newton method for solving the inverse linear second-order cone programming.