Konstantin A. Lurie
Konstantin Lurie has during his professional career made fundamental scientific contributions that have great international influence. His outstanding research contributions in the calculus of variations and control of distributed parameter systems applied to optimum structural design of composite materials have had a great impact on the scientific community. His work is not only known worldwide, but it has generated a new research area that continues to involve research groups from around the world.
Lurie obtained his Ph.D. in 1964 from the A.F. Ioffe Physical Technical Institute of the Academy of Sciences in Leningrad with a thesis on Some optimal problems in magneto-hydrodynamics, followed by a doctorate in 1972 from the same Institute entitled An investigation of optimal problems for systems governed by partial differential equations with applications to magneto-hydrodynamics and elasticity. He was a Research Fellow at the Ioffe Physical Technical Institute and Professor at the Leningrad Institute for Naval Architects until 1988. In 1989 he was the Goebel Visiting Professor at the University of Michigan, Ann Arbor, and in the fall of the same year he joined the Mathematical Sciences Department at WPI.
His about 100 papers have had a great scientific impact. The results of his research have been cited by numerous authors, as they have opened new research areas. A few of his seminal, highly cited papers are:
- "Regularization for optimal design problems for bars and plates" (with A. V. Cherkaev and A. V. Fedorov, 1982)
- "G-closure of a set of anisotropically conductive media in the two-dimensional case" (with A. V. Cherkaev, 1984)
- "Invariant properties of the stress in plane elasticity and equivalence classes of composites" (with A. V. Cherkaev and G. W. Milton, 1992)
Lurie has published two books. The more recent book, Applied Optimal Control of Distributed Systems, lays out the modern approach to optimization of distributed systems and reviews its applications, addressing selected issues of the optimal control of systems described by elliptic, hyperbolic, and parabolic equations.
In his early work he discovered a generalization of Pontryagin’s maximum principle, which is pivotal to the treatment of a wide class of optimal control problems. Lurie’s generalization extends the principle to a much broader category of problems governed by partial differential equations by introducing a new canonical form of governing PDEs suitable for a universal formulation. He introduced new necessary conditions for optimality that apply to elliptic systems containing controls in the coefficients. This work led to demonstrating the ill-posedness of problems with controls in the coefficients and led him to the formulation of a new relaxed problem that admits solutions.
Lurie also made the link between "chattering" controls and composite materials, enabling new understanding of the latter. These contributions opened the doors to the modern area of research on structural optimization in the context of relaxation.
Lurie introduced the concept of G-closure of the set of controls, which provides a direct approach to optimization problems with controls in the coefficients. This new approach has produced new exact bounds on the effective properties of composites that add to the classical ones discovered by Clerk Maxwell and Lord Taylor. These bounds are successful at correctly restating the relevant problems of optimal layout of composite materials and are used by many authors to effectively construct optimal layouts for a variety of problems.
Later he introduced a direct approach to non-selfadjoint problems of optimal design, for the cases for which the G-closure is difficult to determine. This approach is based on a special procedure of "quasi-saddleification" introduced by Lurie, which is the analogue for min-max variational problems of the quasiconvexification used for minimal variational problems.
Recently Lurie started to work on dynamic optimization problems. This is a totally new area, and his work is a pioneering effort. The theory applies to "smart materials," as it has been found by Lurie that an appropriate spatio-temporal activation of these materials can result in screening out long-wave dynamic disturbances. The idea of looking at the possibility of controlling the properties of composites in space as well as in time (spatio-temporal composite materials or "dynamic materials") has proven to yield very interesting results and is a new contribution to the smart-material area.
Lurie has been appointed to the editorial boards of two of the most prestigious applied analysis mathematical journals: Journal of Mathematical Analysis and Applications (Academic Press) and the Journal of Optimization Theory and Applications (Plenum). He was the recipient of a Fulbright Scholar Award and was named the John Sinclair Professor of Mathematical Sciences, in recognition of his scientific accomplishments while at WPI.Maintained by email@example.com
Last modified: Jul 21, 2005, 16:03 EDT