Research in optimization attracted attention when significant advances were made in linear programming—the optimization of a linear objective over a linear constraint set—in the late 1940s. The focus of the optimization literature continued to remain in the domain of linearity for the next couple of decades and devoted itself to advancing the field of linear programming and its subclasses (Dantzig 1963, Ahuja, Magnanti & Orlin 1993). Motivated by applications, developments in nonlinear programming algorithms followed quickly and concerned themselves mostly with local optimization guaranteeing globality under certain convexity assumptions (cf. Minoux 1986, Bazaraa, Sherali & Shetty 1993) However, problems in many areas, including engineering design, logistics, manufacturing, and the chemical and biological sciences are often modeled via nonconvex formulations and exhibit multiple local optima.
KeywordsGlobal Optimization Algorithm Optimal Objective Function Partition Element Convex Envelope Nonconvex Problem
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