The class of sufficient matrices is important in the study of the linear complementarity problem(LCP) – some interior point methods (IPM’s) for LCP’s with sufficient data matrices have complexity polynomial in the bit size of the matrix and its handicap. In this paper we show that the handicap of a sufficient matrix may be exponential … Read more
We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes material and labor costs for concrete, steel reinforcing bars, and formwork according to typical contractor methods. Restrictions enforce correct geometry of the cross-section dimensions for each element and relative … Read more
We propose an interior-point algorithm based on an elastic formulation of the L1-penalty merit function for mathematical programs with complementarity constraints. The method generalizes that of Gould, Orban and Toint (2003) and naturally converges to a strongly stationary point or delivers a certificate of degeneracy without recourse to second-order intermediate solutions. Remarkably, the method allows … Read more
We present a pivoting algorithm for solving linear programs with linear complementarity constraints. Our method generalizes the simplex method for linear programming to deal with complementarity conditions. We develop an anticycling scheme that can verify Bouligand stationarity. We also give an optimization-based technique to find an initial feasible vertex. Starting with a feasible vertex, our … Read more
Developing first order optimality conditions for a two-stage stochastic mathematical program with equilibrium constraints (SMPEC) whose second stage problem has multiple equilibria/solutions is a challenging undone work. In this paper we take this challenge by considering a general class of two-stage whose equilibrium constraints are represented by a parametric variational inequality (where the first stage … Read more
In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a system of partial differential variational inequalities. When these inequalities are discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution … Read more
We study the uniform nonsingularity property recently proposed by the authors and present its applications to nonlinear complementarity problems over a symmetric cone. In particular, by addressing theoretical issues such as the existence of Newton directions, the boundedness of iterates and the nonsingularity of B-subdifferentials, we show that the non-interior continuation method proposed by Xin … Read more
We establish results for the problem of tracking a time-dependent manifold arising in online nonlinear programming by casting this as a generalized equation. We demonstrate that if points along a solution manifold are consistently strongly regular, it is possible to track the manifold approximately by solving a linear complementarity problem (LCP) at each time step. … Read more
In this paper we study the class of differential variational inequality(DVI) in a finite-dimension Euclidean space. We study stability and perturbation of the DVI under the OSL condition. Besides, we establish a Prior Bound Theorem, which is a useful tool to prove stability of DVI. In this paper, we replace the classical Lipshitz continuity by … Read more
Parallel iterative methods are power tool for solving large system of linear equations (LQs). The existing parallel computing research results are all most concentred to sparse system or others particular structure, and all most based on parallel implementing the classical relaxation methods such as Gauss-Seidel, SOR, and AOR methods e±ciently on multiprcessor systems. In this … Read more