For contributions to numerical analysis and scientific computing including finite element methods, adaptive methods, reliability, and a posteriori error estimation.

For contributions to systems theory, stochastic control, and communication networks.

For contributions in large-scale nonlinear optimization theory and algorithms, particularly IPOPT, and their novel application to flowsheet optimization, process control, data reconciliation, and complex process applications.

For contributions to numerical linear algebra, especially numerical methods for least squares problems.

For contributions to signal processing, image analysis, and ant robotics.

For contributions to the modeling and analysis of partial differential equations motivated by applications in the life sciences.

For contributions to numerical linear algebra, data analysis, and machine learning.

For contributions to inverse problems, scientific computing, and numerical analysis and their application to hydrocarbon exploration.

For contributions to the mathematics and modeling of the cell, the immune system, and biological swarms, as well as to applied mathematics education.

For contributions to computational science and engineering, industrial collaborations, and mathematical exposition.

For advances in spectral methods, radial basis functions, and other methods for computational fluid dynamics and partial differential equations.

For contributions to optimization of systems governed by partial differential equations and leadership to promote computational science and engineering.

For contributions to numerical optimization, linear algebra, and software.

For contributions to coding theory, data encryption, communications, and mathematical games.

For advances in high-order numerical methods for partial differential equations and applications.

For contributions to the design and analysis of approximation algorithms, flow problems, and their innovative use in applications, and in solving NP-hard problems.

For contributions to semidefinite optimization and complementarity problems.

For contributions to the theory of wavelets and harmonic analysis, and to interior-point and direct search optimization.

For contributions to global polynomial optimization and the generalized problem of moments.

For advances in the theory of shock waves and kinetic theory.

For contributions to multiscale numerical methods for materials with microstructure and defects and atomistic to continuum models.

For contributions to the numerical analysis of systems, control, and data assimilation.

For developing new geometric methods for differential equations leading to applications in fluid mechanics, elasticity, quantum mechanics, and image processing.

For contributions to the fluid dynamics of interfacial instabilities through the mathematical and numerical analysis of viscous, viscoelastic, and thermal effects.

For contributions to finite element methods and scientific computing.

For contributions to the development of mimetic finite difference methods for nonlinear systems of partial differential equations.

For the development of optimization algorithms for groundwater flow and related environmental problems.

For contributions to numerical linear algebra.

For advances in numerical linear algebra, especially iterative methods.

For advancing symbolic and numerical techniques for solving systems of nonlinear polynomial equations and inequalities and connecting computational algebraic geometry with applications.

For advances in mathematical epidemiology of infectious diseases and in mathematics applied in industry problems.

For contributions to the mathematical and numerical analysis of nonlinear problems of PDEs and applications in inverse problems, homogenization, and material science.

*Deceased