Nonlinear Programming Theory and Algorithms

By K. G. Murty. Technometrics, 2007

2,957 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/515112dcfce5bcb8412adc56254f2751788027bd

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Citations in the corpus

Material parameters identification: Gradient-based, genetic and hybrid optimization algorithms (2008, methodology): “One can mention a large number of optimization gradient-based methods such as the Steepest Descent Method, the Newton method or several Quasi-Newton Methods [17–20].”
Introduction to Global Optimization (2006, neutral): “It can be shown that if x ∗ is a constrained minimum then there is no nonzero feasible descent direction at x ∗ (see [BSS93], p. 141).”
Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization (2009, neutral): “ 0 5 10 15 20 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 x 10 4 time (sec) Objective function prox_TV_iterations 5 10 20 40 5, 10 20 40 0 5 10 15 20 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 x 10 4 time (sec) Objective function prox_TV_iterations 5 10 20 40 80 Fig.”
Multiperiod effects of corporate social responsibility on supply chain networks, transaction costs, emissions, and risk (2008, background): “…conditions for all manufacturers i; i = 1, ..., I, simultaneously, can then be expressed as the following variational inequality (cf. Cruz, 2008; Bazaraa et al., 1993; Gabay and Moulin, 1980): determine (Q1∗, η1∗) ∈ K1 satisfying: T∑ t=1 I∑ i=1 J∑ j=1 [ ∂f it (q i∗ t , η 1∗ it ) ∂qijt + ∂cijt(q…”
Mitigating global supply chain risks through corporate social responsibility (2013, positive): “Hence, the optimality conditions for all manufacturers simultaneously (Bazaraa, Sherali, and Shetty 1993; Nagurney 1999; Cruz 2008) can be expressed as the following variational inequality: determine ðQ1 ; g1 Þ 2 RILðKHLþ1Þþ , which satisfies XI i¼1 XL l¼1 XK k¼1 XH h¼1 XL l¼1 @F̂ ilðqil ; gil Þ…”
Biconvex sets and optimization with biconvex functions: a survey and extensions (2007, background): “For a general definition of algorithmic maps we refer to Bazaraa et al. (1993).”
Distributionally Robust Optimization: A Review (2019, neutral): “[16], Bertsekas [30], Ruszczyński [269], Rockafellar [257].”
Penalty Function Methods for Constrained Optimization with Genetic Algorithms (2005, background): “Using these definitions, nonlinear programming problem is to find a point F x ∈ such that ) x ( f ) x ( f * ≤ for all F x∈ [3].”
Big data for cyber physical systems in industry 4.0: a survey (2019, background): “…as stochastic programming with random variables (Birge and Louveaux 2011), dynamic programming for questions that can be divided into smaller problems (Bellman 2013), and nonlinear programming with non-linear functions in either objective function or constraints (Bazaraa, Sherali, and Shetty 2013).”
Stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications (2008, neutral): “, [5].”
A Complementarity Model for the European Natural Gas Market (2007, background): “These players, except for LNG tankers, marketers and consumers, are modeled via convex optimization problems, whose Karush-Kuhn-Tucker (KKT) optimality conditions [2] are both necessary and su¢ cient for global optimality.”
Optimization approach to real power tracing: an application to transmission fixed cost allocation (2006, background): “Remark 7: This problem is an LAV minimization problem that can be converted to an LP problem as explained in [22].”
On energy provisioning and relay node placement for wireless sensor networks (2005, neutral): “Let us examine the following simplified problem.”
Predictive Control for Linear and Hybrid Systems (2017, methodology): “2 Geometric interpretation of KKT conditions [27].”
Convex Principal Feature Selection (2010, background): “One can solve it with any favorite optimization algorithm [11, 12].”