Linear Complementarity Problem Research Papers (original) (raw)

This paper is concerned with the development of an improvement algorithm for the Linear Complementarity Problem (LCP). Our approach to find a solution to LCP is to solve the equivalent Constrained Optimization Problem (COP) of maximizing... more

This paper is concerned with the development of an improvement algorithm for the Linear Complementarity Problem (LCP). Our approach to find a solution to LCP is to solve the equivalent Constrained Optimization Problem (COP) of maximizing the sum of the minimum of each complementary pair of variables, subject to the constraints that each such minimum is nonpositive.The algorithm, ascent in nature, is similar to the simplex method in the sense that it moves between basic points of an associated system of linear equations. These basic points are feasible to our COP whose objective function is piecewise linear and concave. Classes of matrices are characterized for which our algorithm processes LCP for every right hand side vector and every matrix in the class. A computational study shows that our algorithm is clearly superior to a previos improvement algorithm. Computational comparisons with Lemke's well known algorithm are also presented.

A brief but concise review of methods to generate P-matrices (i.e., matrices having positive principal minors) is provided and motivated by open problems on P-matrices and the desire to develop and test efficient methods for the detection... more

A brief but concise review of methods to generate P-matrices (i.e., matrices having positive principal minors) is provided and motivated by open problems on P-matrices and the desire to develop and test efficient methods for the detection of P-matrices. Also discussed are operations that leave the class of P-matrices invariant. Some new results and extensions of results regarding P-matrices are included.

A linear complementarity problem (LCP) is formulated for the price of American options under the Bates model which combines the Heston stochastic volatility model and the Merton jump-diffusion model. A finite difference discretization is... more

A linear complementarity problem (LCP) is formulated for the price of American options under the Bates model which combines the Heston stochastic volatility model and the Merton jump-diffusion model. A finite difference discretization is described for the partial derivatives and a simple quadrature is used for the integral term due to jumps. A componentwise splitting method is generalized for the Bates model. It is leads to solution of sequence of one-dimensional LCPs which can be solved very efficiently using the Brennan and Schwartz algorithm. The numerical experiments demonstrate the componentwise splitting method to be essentially as accurate as the PSOR method, but order of magnitude faster. Furthermore, pricing under the Bates model is less than twice more expensive computationally than under the Heston model in the experiments.

... For example, a finite difference method is used in [2], [15], [16], [24], a finite element method is considered in [28], and a finite volume method in [10]. The Black-Scholes partial differential equation contains variable... more

... For example, a finite difference method is used in [2], [15], [16], [24], a finite element method is considered in [28], and a finite volume method in [10]. The Black-Scholes partial differential equation contains variable coefficients for the first-order and second-order spatial ...

With the overexploitation of many conventional fish stocks, and growing interest in harvesting new kinds of food from the sea, there is an increasing need for managers of fisheries to take account of interactions among species. In this... more

With the overexploitation of many conventional fish stocks, and growing interest in harvesting new kinds of food from the sea, there is an increasing need for managers of fisheries to take account of interactions among species. In this work we define a bioeconomic equilibrium model for 'n' fishermen who catch three species; these species compete with each other for space or food. The natural growth of each species is modeled using a logistic law. The objective of the work is to find the fishing effort that maximizes the profit of each fisherman constrained by the conservation of the biodiversity. The existence of the steady states and its stability are studied using eigenvalue analysis. The problem of determining the equilibrium point that maximizes the profit of each fisherman is then solved by using the generalized Nash equilibrium problem. Finally, some numerical simulations are given to illustrate the results.

Biomass co-firing systems in power plants generate electric power by the simultaneous combustion of biomass and fossil fuels. The co-firing process reduces investment costs by converting biomass energy into electricity in existing... more

Biomass co-firing systems in power plants generate electric power by the simultaneous combustion of biomass and fossil fuels. The co-firing process reduces investment costs by converting biomass energy into electricity in existing conventional power plants. Biomass co-firing significantly reduces carbon dioxide and sulfur dioxide emissions in power generation. To meet the increase in biomass demand, this paper has considered systematic energy crop production, which is expected to increase in the near future. Our aim is to analyze biomass co-firing systems in the Taiwanese electricity market. In this paper, we study two emerging biomass feedstocks: switchgrass and Miscanthus. We focus on the impact of energy crop co-firing on carbon dioxide and sulfur dioxide emissions for electricity generation. A Nash–Cournot competition model, which simulates potential biomass co-firing scenarios, is formulated for power markets. A case study conducted in the Taiwanese electricity market showed that biomass co-firing lowers total electricity demand and sale. Miscanthus is more economical than switchgrass in terms of the production cost and the land required to generate biopower for the same levels of biomass co-firing.► Biomass co-firing system in electricity market is analyzed in this paper. ► The research studies the impact of two energy crops in co-firing system. ► This paper conducts a case study of co-firing system in Taiwan power markets.

Interior Point Methods not only are the most effective methods in practice but also have polynomial-time complexity. The large update interior point methods perform in practice much better than the small update methods which have the best... more

Interior Point Methods not only are the most effective methods in practice but also have polynomial-time complexity. The large update interior point methods perform in practice much better than the small update methods which have the best known theoretical complexity. In this paper, motivated by the complexity results for linear optimization based on kernel functions, we extend a generic primal

This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations... more

This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improvement of a method described by Kocvara and Zowe (Numer Math 68:95–106, 1994) that combines projected Gauss–Seidel iterations with subspace minimization steps. The proposed algorithm employs a recursive subspace minimization designed to handle severely ill-conditioned problems. Numerical tests indicate that the approach is more efficient than interior-point and gradient projection methods on some physical simulation problems that arise in computer game scenarios.

We present a fluid simulation method based on Smoothed Particle Hydrodynamics (SPH) in which incompressibility and boundary conditions are enforced using holonomic kinematic constraints on the density. This formulation enables systematic... more

We present a fluid simulation method based on Smoothed Particle Hydrodynamics (SPH) in which incompressibility and boundary conditions are enforced using holonomic kinematic constraints on the density. This formulation enables systematic multiphysics integration in which interactions are modeled via similar constraints between the fluid pseudoparticles and impenetrable surfaces of other bodies. These conditions embody Archimede's principle for solids and thus buoyancy results as a direct consequence. We use a variational time stepping scheme suitable for general constrained multibody systems we call SPOOK. Each step requires the solution of only one Mixed Linear Complementarity Problem (MLCP) with very few inequalities, corresponding to solid boundary conditions. We solve this MLCP with a fast iterative method. Overall stability is vastly improved in comparison to the unconstrained version of SPH, and this allows much larger time steps, and an increase in overall performance by ...

The Cournot model is a common and reasonable approximation to representing strategic competition in electricity markets. This paper proposes a Nash-Cournot model in which unit outages and fuel cost volatility are both accounted for. The... more

The Cournot model is a common and reasonable approximation to representing strategic competition in electricity markets. This paper proposes a Nash-Cournot model in which unit outages and fuel cost volatility are both accounted for. The Nash equilibrium quantity of each firm is obtained by maximizing its expected profit given the distribution of fuel costs and the availability of generating units. The Cournot equilibrium problem is formulated as a linear complementarity problem. We give a numerical example to show how the price, equilibrium quantities, and firms' profits are affected when outages and fuel cost volatility are ignored.

We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and... more

We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of K-matrices to the setting of oriented matroids. Our proof is elementary and simplifies the original proof substantially by exploiting the duality of oriented matroids. As an application, we show that a simple principal pivot method applied to the linear complementarity problems with K-matrices converges very quickly, by a purely combinatorial argument.