Optimization: Algorithms and Consistent Approximations

By Elijah Polak. 1997

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Citations in the corpus

Pseudospectral Optimal Control and Its Convergence Theorems (2008, methodology): “One is based on the theory of consistent approximations [17] and the other based on Robinson’s implicit function theorem [20, 21].”
Global convergence of a modified Fletcher–Reeves conjugate gradient method with Armijo-type line search (2006, methodology): “[32] proposed a descent modified Polak–Ribière–Polyak (PRP) method [24,26], i.”
An analysis of particle swarm optimizers (2002, methodology): “Some of the better known algorithms include FletcherReeves (FR), Polar-Ribiere (PR), Davidon-Fletcher-Powell (DFP), Broyden-FletcherGoldfarb-Shanno (BFGS) [104, 11].”
Optimization algorithms exploiting unitary constraints (2002, methodology): “The second type of algorithm derived in this paper is based on the traditional Newton algorithm [22].”
Retrospective on optimization (2004, unknown): “A number of studies have shown (e.g., Cuthrell & Biegler, 1989; Polak, 1997; Reddien, 1979; Schwartz, 1996) that the KKT conditions of the simultaneous NLP can be made consistent with the optimality conditions of the variational problem.”
Constrained model predictive control: Stability and optimality (2000, unknown): “Many optimal control algorithm have been developed; see, for example, (Polak, 1997).”
A survey on approaches for reliability-based optimization (2010, methodology): “Thus, the RBO problem can be solved most efficiently using specialized algorithms for semi-infinite programming problems (Polak, 1997). Two types of problems are studied: the minimization of a deterministic function subjected to a number of reliability constraints and the maximization of the reliabi”
Generalized semi-infinite programming: A tutorial (2008, methodology): “As an example we mention the Polak–He algorithm and refer the reader to [ 68, Section 2.6 ] for details.”
Semi-infinite programming, duality, discretization and optimality conditions (2009, unknown): “, [4, 9, 10, 22, 23, 31]).”
A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization (2004, methodology): “Discrete Armijo gradient algorithm We used the discrete Armijo gradient algorithm from [7], which can be used to minimize smooth functions.”
Optimal mode-switching for hybrid systems with varying initial states (2008, methodology): “The theory of min-max optimization and consistent approximations [20] can be utilized in order to implement and solve this problem.”
Characterization and computation of local Nash equilibria in continuous games (2013, methodology): “By generalizing derivative–based conditions for local optimality in nonlinear programming [14] and optimal control [15], we provide necessary first– and second–order conditions that local Nash equilibria must satisfy, and further develop a second–order sufficient condition ensuring player strategies”
Spherical averages and applications to spherical splines and interpolation (2001, background): “6 of Polak [1997]. We have u=Hv, so by the comments after Theorem 6, 1 ≥ v ·u > 2 for some 2 > 0 in some neighborhood of qsoln. From this it can be shown, again in a sufficiently small neighborhood of qsoln, that if q′ = expq(q+u), then f (q′)<δ f (q) for some 0<δ<1. This implies that A1 converges a”