Solution Analysis for the Pseudomonotone Second-order Cone Linear Complementarity Problem

In this paper, we study properties of the solution of the pseudomonotone second-order cone linear complementarity problems (SOCLCP). Based upon Tao’s recent work [Tao, J. Optim. Theory Appl., 159(2013), pp. 41–56] on pseudomonotone LCP on Euclidean Jordan algebras, we made two noticeable contributions on the solutions of the pseudomonotone SOCLCP: First, we introduce the concept … Read more

A Filter Active-Set Algorithm for Ball/Sphere Constrained Optimization Problem

In this paper, we propose a filter active-set algorithm for the minimization problem over a product of multiple ball/sphere constraints. By making effective use of the special structure of the ball/sphere constraints, a new limited memory BFGS (L-BFGS) scheme is presented. The new L-BFGS implementation takes advantage of the sparse structure of the Jacobian of … Read more


Recently, the globally uniquely solvable (GUS) property of the linear transformation $M\in R^{n\times n}$ in the second-order cone linear complementarity problem (SOCLCP) receives much attention and has been studied substantially. Yang and Yuan [30] contributed a new characterization of the GUS property of the linear transformation, which is formulated by basic linear-algebra-related properties. In this … Read more

Optimality conditions for the nonlinear programming problems on Riemannian manifolds

In recent years, many traditional optimization methods have been successfully generalized to minimize objective functions on manifolds. In this paper, we first extend the general traditional constrained optimization problem to a nonlinear programming problem built upon a general Riemannian manifold $\mathcal{M}$, and discuss the first-order and the second-order optimality conditions. By exploiting the differential geometry … Read more

An efficient matrix splitting method for the second-order cone complementarity problem

Given a symmetric and positive (semi)definite $n$-by-$n$ matrix $M$ and a vector, in this paper, we consider the matrix splitting method for solving the second-order cone linear complementarity problem (SOCLCP). The matrix splitting method is among the most widely used approaches for large scale and sparse classical linear complementarity problems (LCP), and its linear convergence … Read more


In this paper, we consider the solution of the standard linear programming (LP). A remarkable result in LP claims that all optimal solutions form an optimal face of the underlying polyhedron. In practice, many real-world problems have infinitely many optimal solutions and pursuing the optimal face, not just an optimal vertex, is quite desirable. The … Read more

The Globally Uniquely Solvable Property of Second-Order Cone Linear Complementarity Problems

The globally uniquely solvable (GUS) property of the linear transformation of the linear complementarity problems over symmetric cones has been studied recently by Gowda et al. via the approach of Euclidean Jordan algebra. In this paper, we contribute a new approach to characterizing the GUS property of the linear transformation of the second-order cone linear … Read more