Random Test Problems and Parallel Methods for Quadratic Programs and Quadratic Stochastic Programs
نویسنده
چکیده
This paper proposes a data parallel procedure for randomly generating test problems for two-stage quadratic stochastic programming. Multiple quadratic programs in the second stage are randomly generated in parallel. A solution of the quadratic stochastic program is determined by multiple symmetric linear complementarity problems. The procedure allows the user to specify the size of the problem, the condition numbers of the Hessian matrices of the objective functions and the structure of the feasible regions in the rst and the second stages. These test problems are used to evaluate three parallel algorithms for multiple quadratic programs and a parallel inexact Newton method for quadratic stochastic programming. Numerical experiments on a Thinking Machine CM-5, Silicon Graphics Power Challenge, and DEC Alpha Server are reported.
منابع مشابه
Parallel interior-point solver for structured quadratic programs: Application to financial planning problems
Issues of implementation of a library for parallel interior-point methods for quadratic programming are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modeled. The efficiency of the solver is illustrated on se...
متن کاملA Polynomial-Time Solution Scheme for Quadratic Stochastic Programs
We consider quadratic stochastic programs with random recourse — a class of problems which is perceived to be computationally demanding. Instead of using mainstream scenario tree-based techniques, we reduce computational complexity by restricting the space of recourse decisions to those linear and quadratic in the observations, thereby obtaining an upper bound on the original problem. To estima...
متن کاملParallel Interior-Point Method for Linear and Quadratic Programs with Special Structure
This paper concerns the use of iterative solvers in interiorpoint methods for linear and quadratic programming problems. We state an adaptive termination rule for the inner iterative scheme and we prove the global convergence of the obtained algorithm, exploiting the theory developed for inexact Newton methods. This approach is promising for problems with special structure on parallel computers...
متن کاملA Parallel Inexact Newton Method for Stochastic Programs with Recourse
A parallel inexact Newton method with a line search is proposed for two-stage quadratic stochastic programs with recourse. A lattice rule is used for the numerical evaluation of multi-dimensional integrals, and a parallel iterative method is used to solve the quadratic programming subproblems. Although the objective only has a locally Lipschitz gradient, global convergence and local superlinear...
متن کاملA New Mathematical Approach based on Conic Quadratic Programming for the Stochastic Time-Cost Tradeoff Problem in Project Management
In this paper, we consider a stochastic Time-Cost Tradeoff Problem (TCTP) in PERT networks for project management, in which all activities are subjected to a linear cost function and assumed to be exponentially distributed. The aim of this problem is to maximize the project completion probability with a pre-known deadline to a predefined probability such that the required additional cost is min...
متن کامل