Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques

By Ignacio E. Grossmann. 2002

664 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/dffedac9e541a3cef84ff22279cae7f20be65a50

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Citations in the corpus

Optimization Models for Machine Learning: A Survey (2019, methodology): “In [64], the problem of computing maximum perturbation bounds for DNNs is formulated as a MIP, where indicator constraints and disjunctive constraints are modeled using constraints with big-M coefficients [109].”
The Benders decomposition algorithm: A literature review (2017, methodology): “A major advantage of the LBBD method is that the subproblem needs not take a specific form: it can be an MILP (Jain and Grossmann, 2001), a CP (Hooker, 2005), an NLP (Wheatley et al., 2015), or a feasibility-checking problem (Harjunkoski and Grossmann, 2002).”
State-Of-The-Art Review of Mathematical Optimisation Approaches for Synthesis of Energy Systems (2017, background): “Mathematical models range from the relatively straightforward linear programming (LP) to increasingly complex mixed-integer linear programming (MILP), non-linear programming (NLP) and mixed-integer non-linear programming (MINLP), which depict real-life scenarios more accurately (Grossmann 2002).”
Optimization-Based Collision Avoidance (2017, background): “ensure collision avoidance, which is often reformulated as a mixed-integer optimization problem [1], [4], [16].”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “convex programs based on the reformulation-linearization technique: see Rikun (1997), Sherali (1997), Sherali and Tuncbilec (1995, 1997a, 1997b), Al-Khayyal, Larsen and van Voorhis (1995), and Audet, Hansen, Jaumard and Savard (2000). Also related is the lift-and-project technique in mixed integer l”
State-of-the-art review of optimization methods for short-term scheduling of batch processes (2006, methodology): “Although a more efficient logicbased approach was also presented in Pinto and Grossmann (1997), we only focused our attention on the pure MILP approach. Since the set of new variables and constraints for modeling resource limitations notably increases the model complexity, preordering rules were emb”
Mixed-integer nonlinear optimization*† (2013, methodology): “We mention a number of surveys and monographs on MINLP, including a review of MINLP and disjunctive programming (Grossmann, 2002), a survey of MINLP algorithms (Grossmann and Kravanja, 1997), a survey of algorithms and software for MINLP (Bonami et al.”
Maximum Resilience of Artificial Neural Networks (2017, methodology): “The non-linearity in ReLU constraints x i ) is handled using the well-known big-M method [10], which introduces a binary integer variable b i .”
Branching and bounds tighteningtechniques for non-convex MINLP (2009, background): “The reader may refer to [39, 78, 79], the surveys [36, 45], and references therein for a general introduction on MINLP solvers.”
A Conic Representation of the Convex Hull of Disjunctive Sets and Conic Cuts for Integer Second Order Cone Optimization (2015, methodology): “Disjunctive methods in mixed integer linear optimization have been studied extensively during the past decades [4, 5, 13, 17].”