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Convex Optimization and ApplicationsOptimization
|Speaker: ||Steve Boyd, Stanford University|
|Location: ||2112 MSB|
|Start time: ||Fri, Mar 10 2006, 2:10PM|
In this talk I will give an overview of some major developments in
convex optimization that have emerged over the last ten years or so,
and briefly describe several typical applications.
The basic idea is that convex problems are fundamentally tractable,
in theory and in practice. The polynomial worst-case complexity
results of linear programming have been extended to nonlinear convex
optimization, and interior-point methods for nonlinear convex
optimization achieve efficiencies approaching that of modern linear
programming solvers. Several new classes of standard convex
optimization problems have emerged, including semidefinite programming, determinant maximization, second-order cone programming, and
geometric programming. Like linear and
quadratic programming, we have a fairly complete duality theory, and
very effective numerical methods for these problem classes.
There has been a steadily expanding list of new applications of convex
optimization, in areas such as circuit design, signal processing,
statistics, communications, control, and other fields.
Convex optimization is also emerging as an
important tool for hard, non-convex problems.
Convex relaxations of hard problems provide a general approach
for handling hard optimization problems, with applications in
combinatorial optimization and robust optimization.
Joint work with Lieven Vandenberghe