Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

By Mohit Tawarmalani, Nikolaos V. Sahinidis. 2002

797 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/343a64a645c85497d33a364a003c6926308069ed

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In Numerical Analysis

Citations in the corpus

A Flexible Mixed-Integer Linear Programming Approach to the AC Optimal Power Flow in Distribution Systems (2014, background): “Problems of this class are usually difficult to treat computationally, and even the continuous relaxation of a non-convex MINLP is a global optimization problem [74], likely to be NP-hard (non-deterministic polynomial-time hard) [75].”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “Because linear programming solvers are currently much more reliable and faster than general convex solvers, the convex envelopes used in BARON are in fact approximated by a number of linear constraints computed adaptively with a variant of the sandwich algorithm of Rote et al. (Burkard, Hamacher and”
Optimization under uncertainty: state-of-the-art and opportunities (2004, background): “Recent developments in the area of global optimization (Tawarmalani & Sahinidis, 2002 ) are thus very likely to play a major role towards the solution of optimization problems under uncertainty.”
Branching and bounds tighteningtechniques for non-convex MINLP (2009, methodology): “Although this technique is well known in the Global Optimization community, we describe it in detail to introduce notation and concepts that are useful to discuss other features of couenne .”
On handling indicator constraints in mixed integer programming (2016, methodology): “a common tightening technique in MILP and MINLP solvers (see [19], and [3] and [21], respectively.”
MINLP Solver Software (2011, background): “MISQP and OQNLP can handle general MINLPs, but do not guarantee global optimality even on convex problems.”
Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization (2007, positive): “While there is no guarantee of optimality and no “gap” is available, it can be combined with other algorithms that provide this information, e.g., LGO(Pinter 2004) or BARON ( Tawarmalani and Sahinidis 2002 ).”
Certifiably Optimal Low Rank Factor Analysis (2016, methodology): “…optimization problems, quadratically-constrained convex optimization problems, and bi-linear optimization problems (Hansen et al., 1993; Bao et al., 2009; Tawarmalani and Sahinidis, 2002b; Tawarmalani et al., 2013; Costa and Liberti, 2012; Anstreicher and Burer, 2010; Misener and Floudas, 2012).”
Optimal constrained control allocation in marine surface vessels with rudders (2003, methodology): “Keywords: Ship control, multi-parametric programming, disjunctive programming.”