Non-convex mixed-integer nonlinear programming: A survey

By S. Burer, Adam N. Letchford. 2012

623 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

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Citations in the corpus

Strongly agree or strongly disagree?: Rating features in Support Vector Machines (2016, background): “We can formulate the DILSVM as the following Discrete Quadratic Programming problem: min ω, b, ξ 1 2 d∑ j=1 ω2j + C n n∑ i=1 ξi (1) s.t. yi(ω >xi + b) ≥ 1− ξi ∀i = 1, . . . , n (2) ωj ∈ A ∀j = 1, . . . , d (3) b ∈ R (4) ξi ≥ 0 ∀i = 1, . . . , n. (5) See Burer and Letchford (2012) for a recent review”
Mixed Integer Linear Programming Formulation Techniques (2015, methodology): “They are an important tool for nonconvex mixed integer nonlinear programming [29] and have been extensively studied in the context of mathematical programming reformulations [109, 108].”
A robust optimization approach for dynamic traffic signal control with emission considerations (2012, background): “If, in addition, any of the objective and/or constraint functions become nonconvex, the problem will become extremely challenging to solve, or, sometimes, even to identify a feasible solution (Burer and Letchford, 2012).”
Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface With Discrete Phase Shifts (2019, methodology): “As such, all the possible values of φi,n are restricted to the set F and accordingly we have φi,n=aTyi,n−2πεi,n, cos(φi,n)=cTyi,n, sin(φi,n)=sTyi,n. (22) Substituting (21) and (22) into problem (18), we obtain the following optimization problem max {xn},{yi,n},{εi,n} N−1 i=1 N n=i+1 2|A(i, n)| cos(a”
ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations (2014, background): “Tables 24–43 in the online supplement give the results of the computational study with 2 , 571 total problems; Fig.”