An interior algorithm for nonlinear optimization that combines line search and trust region steps

By Richard A. Waltz, Jose Luis Morales, Jorge Nocedal, Dominique Orban. Mathematical programming, 2006

1,139 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5a80871bd050485b65ae3ebb437998c6ef17000d

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Knitro: An Integrated Package for Nonlinear Optimization (2006, methodology): “As shown in [38] this stronger condition can improve performance of the line search iteration.”
Load frequency control of a two-area multi-source power system using a tilt integral derivative controller (2018, background): “Detailed information regarding the numerical solution of optimality conditions can be found in Byrd et al. (1999) and Waltz et al. (2006).”
Recent advances in trust region algorithms (2015, neutral): “Otherrecentworksontrustregioninterior-pointmethodsinclude[129], [139]and[71].”
Entropy Search for Information-Efficient Global Optimization (2011, methodology): “For reference, we also compare to a number of numerical optimization algorithms: Trust-Region-Reflective (Coleman and Li, 1996, 1994), Active-Set (Powell, 1978b,a), interior point (Byrd et al., 1999, 2000; Waltz et al., 2006), and a naı̈vely projected version of the BFGS algorithm (Broyden, 1965; Fl”
A Kernel-Based Feature Selection Method for SVM With RBF Kernel for Hyperspectral Image Classification (2014, background): “Equations (10) and (11) are the unconstrained nonlinear optimization problem so that some popular optimization algorithms [29]–[31] can be employed to solve this problem.”
Analysis of directional dependence using asymmetric copula-based regression models (2014, methodology): “Thus, we obtain the MPLE for φ by using constrained nonlinear algorithms such as interior-point algorithm [20] and active-set algorithm [21] provided by the MATLAB function, ‘fmincon’.”
Numerical lower bound shakedown analysis of engineering structures (2011, methodology): “Among the different approaches for the solution of nonlinear optimization problems, we choose the widely used interior-point method [8–11], which has been implemented into several software packages for general nonlinear programming, such as LOQO [12,13], KNITRO [14,15] and IPOPT [16,17].”