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Nocedal is well-known for his research in nonlinear optimization, particularly for his work on L-BFGS [4] [5] and his textbook Numerical Optimization. [6] In 2001, Nocedal co-founded Ziena Optimization Inc. and co-developed the KNITRO software package. [7] Nocedal was a chief scientist at Ziena Optimization Inc. from 2002 to 2012 before the ...
The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting of a parabola to the graph of () at the trial value , having the same slope and curvature as the graph at that point, and then proceeding to the maximum or minimum of that parabola (in higher dimensions, this may also be a saddle point), see below.
Compared with Wolfe's conditions, which is more complicated, Armijo's condition has a better theoretical guarantee. Indeed, so far backtracking line search and its modifications are the most theoretically guaranteed methods among all numerical optimization algorithms concerning convergence to critical points and avoidance of saddle points, see ...
The optimization of portfolios is an example of multi-objective optimization in economics. Since the 1970s, economists have modeled dynamic decisions over time using control theory . [ 14 ] For example, dynamic search models are used to study labor-market behavior . [ 15 ]
For large-scale optimization, the Gauss–Newton method is of special interest because it is often (though certainly not always) true that the matrix is more sparse than the approximate Hessian . In such cases, the step calculation itself will typically need to be done with an approximate iterative method appropriate for large and sparse ...
Nocedal, Jorge and Wright, Stephen J. (1999). Numerical Optimization. Springer. ISBN 0-387-98793-2. Jan Brinkhuis and Vladimir Tikhomirov, Optimization: Insights and Applications, 2005, Princeton University Press
Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems. [1] It is related to, but distinct from, quasi-Newton methods .
Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective, but the augmented Lagrangian method adds yet another term designed to mimic a Lagrange multiplier.
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