David R. Easterling

Solving the canonical dual of box-and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm

This paper presents a massively parallel global deterministic direct search method (VTDIRECT) for solving nonconvex quadratic minimization problems with either box or±1 integer constraints. Using the canonical dual transformation, these well-known NP-hard problems can be reformulated as perfect dual stationary problems (with zero duality gap). Under certain conditions, these dual problems are equivalent to smooth concave maximization over a convex feasible space. Based on a perturbation method proposed by Gao, the integer programming problem is shown to be equivalent to a continuous unconstrained Lipschitzian global optimization problem. The parallel algorithm VTDIRECT is then applied to solve these dual problems to obtain global minimizers. Parallel performance results for several nonconvex quadratic integer programming problems are reported.

Parallel deterministic and stochastic global minimization of functions with very many minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University.

Results of two global optimization algorithms applied to a problem in biomechanics

The results of two global optimization algorithms applied to an optimization problem in biomechanics are presented. Of interest is the discovery of the minimum value of an objective function derived from certain performance criteria related to a problem in biomechanics---specifically, a biomedical application called perturbation-based balance training (PBBT). PBBT is a method for improving balance through repeated exposure to postural perturbations. A parallel implementations of Spalls algorithm and a parallel implementation of the DIRECT (DIviding RECTangles) algorithm is applied to this optimization problem.

Power saving experiments for large-scale global optimisation

Green computing, an emerging field of research that seeks to reduce excess power consumption in high-performance computing, is gaining popularity among researchers. Research in this field often relies on simulation or only uses a small cluster, typically 8 or 16 nodes, because of the lack of hardware support. In contrast, System G at Virginia Tech is a 2592 processor supercomputer equipped with power-aware components suitable for large-scale green computing research. DIRECT is a deterministic global optimisation algorithm, implemented in the mathematical software package VTDIRECT95. This paper explores the potential energy savings for the parallel implementation of DIRECT, called pVTdirect, when used with a large-scale computational biology application, parameter estimation for a budding yeast cell cycle model, on System G. Two power-aware approaches for pVTdirect are developed and compared against the CPUSPEED power saving system tool. The results show that knowledge of the parallel workload of the underlying application is beneficial for power management.

An SMP soft classification algorithm for remote sensing

This work introduces a symmetric multiprocessing (SMP) version of the continuous iterative guided spectral class rejection (CIGSCR), a semi-automated classification algorithm for remote sensing (multispectral) images. The algorithm uses soft data clusters to produce a soft classification containing inherently more information than a comparable hard classification at an increased computational cost. Previous work suggests that similar algorithms achieve good parallel scalability, motivating the parallel algorithm development work here. Experimental results of applying parallel CIGSCR to an image with approximately 108 pixels and 6 bands demonstrate superlinear speedup. A soft two class classification is generated in just over four minutes using 32 processors.

A Globally Convergent Probability-One Homotopy for Linear Programs with Linear Complementarity Constraints

A solution of the standard formulation of a linear program with linear complementarity constraints (LPCC) does not satisfy a constraint qualification. A family of relaxations of an LPCC, associated with a probability-one homotopy map, proposed here is shown to have several desirable properties. The homotopy map is nonlinear, replacing all the constraints with nonlinear relaxations of NCP functions. Under mild existence and rank assumptions, (1) the LPCC relaxations RLPCC(

Studying Constrained Clustering Problems Using Homotopy Maps

\lambda

The Direct Algorithm Applied to a Problem in Biomechanics with Conformal Mapping.

) have a solution for

Probability-one homotopy maps for tracking constrained clustering solutions

0\le\lambda \le1

Fortran 95 implementation of QNSTOP for global and stochastic optimization

; (2) RLPCC(1) is equivalent to LPCC; (3) the Kuhn--Tucker constraint qualification is satisfied at every local or global solution of RLPCC(