Preconditioning Newton-Krylov Methods in Non-Convex Large Scale Optimization

We consider an iterative preconditioning technique for non-convex large scale optimization. First, we refer to the solution of large scale indefinite linear systems by using a Krylov subspace method, and describe the iterative construction of a preconditioner which does not involve matrices products or matrices storage. The set of directions generated by the Krylov subspace method is used, as by product, to provide an approximate inverse preconditioner. Then, we experience our preconditioner within Truncated Newton schemes for large scale unconstrained optimization, where we generalize the truncation rule by Nash–Sofer (Oper. Res. Lett. 9:219–221, 1990) to the indefinite case, too. We use a Krylov subspace method to both approximately solve the Newton equation and to construct the preconditioner to be used at the current outer iteration. An extensive numerical experience shows that the proposed preconditioning strategy, compared with the unpreconditioned strategy and PREQN (Morales and Nocedal in SIAM J. Optim. 10:1079–1096, 2000), may lead to a reduction of the overall inner iterations. Finally, we show that our proposal has some similarities with the Limited Memory Preconditioners (Gratton et al. in SIAM J. Optim. 21:912–935, 2011)

Digital game elements, user experience and learning

The primary aim of this paper is to identify and theoretically validate the relationships between core game design elements and mechanics, user motivation and engagement and consequently learning. Additionally, it tries to highlight the moderating role of player personality traits on learning outcomes and acceptance and suggest ways to incorporate them in the game design process. To that end, it outlines the role of narrative, aesthetics and core game mechanics in facilitating higher learning outcomes through intrinsic motivation and engagement. At the same time, it discusses how player goal orientation, openness to experience, conscientiousness, sensation seeking and need for cognition influence the translation of the gameplay experience into valuable learning outcomes and user acceptance of the technology

Determination of the mechanical properties of a solid elastic medium from a seismic wave propagation using two statistical estimators

In this paper, we study an inverse problem consisting in the determination of the mechanical properties of a layered solid elastic medium in contact with a fluid medium by measuring the variation of the pressure in the fluid while propagating a seismic-acoustic wave. The estimation of mechanical parameters of the solid is obtained from the simulation of a seismic wave propagation model governed by a system of partial differential equations. Two stochastic methods, Markov chain Monte Carlo with an accelerated version and simultaneous perturbation stochastic approximation, are implemented and compared with respect to cost and accuracy. © 2008 Sage Publications.Al Khoury P, 2005, INVERSE PROBL SCI EN, V13, P219, DOI 10.1080-10682760412331323143; ASSOUS F, 1990, INVERSE PROBL, V6, P487, DOI 10.1088-0266-5611-6-4-003; BISHOP TN, 1985, GEOPHYSICS, V50, P903, DOI 10.1190-1.1441970; BJORCK A, 1996, NUMERICAL METHODS LE; Cerveny V, 2001, SEISMIC RAY THEORY; Christen JA, 2005, J COMPUT GRAPH STAT, V14, P795, DOI 10.1198-106186005X76983; Diaz J, 2005, J COMPUT ACOUST, V13, P403, DOI 10.1142-S0218396X05002736; Gerencser L, 2001, IEEE DECIS CONTR P, P4400, DOI 10.1109-CDC.2001.980894; Ma CC, 2002, J ACOUST SOC AM, V112, P811, DOI 10.1121-1.1496763; Maryak JL, 2001, P AMER CONTR CONF, P756, DOI 10.1109-ACC.2001.945806; MEYER S, 2001, PHYS REV, P3535; NIEDERREITER H, 1992, CBMS NSF REGIONAL C, V63, P241; Plessix RE, 2006, GEOPHYS J INT, V167, P495, DOI 10.1111-j.1365-246X.2006.02978.x; Robert C., 1996, METHODES MONTE CARLO; Spall J. C., 2003, INTRO STOCHASTIC SEA; SPALL JC, 1992, IEEE T AUTOMAT CONTR, V37, P332, DOI 10.1109-9.119632; Spall JC, 1998, IEEE T AERO ELEC SYS, V34, P817, DOI 10.1109-7.705889; TAN MS, PHYS 707SC COURSE MA, pCH7; Tarantola A., 2005, INVERSE PROBLEM THEO; TSOGKA C, 1999, THESIS U PARIS DAUPH, pCH133