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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 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 ]
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method.SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable, but not necessarily convex.
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
In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem.
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.
It is a direct search method (based on function comparison) and is often applied to nonlinear optimization problems for which derivatives may not be known. However, the Nelder–Mead technique is a heuristic search method that can converge to non-stationary points [ 1 ] on problems that can be solved by alternative methods.
Nonlinear programming — the most general optimization problem in the usual framework Special cases of nonlinear programming: See Linear programming and Convex optimization above; Geometric programming — problems involving signomials or posynomials Signomial — similar to polynomials, but exponents need not be integers