Extended formulations for convex envelopes

In this work we derive explicit descriptions for the convex envelope of nonlinear functions that are component-wise concave on a subset of the variables and convex on the other variables. These functions account for more than 30% of all nonlinearities in common benchmark libraries. To overcome the combinatorial difficulties in deriving the convex envelope description given by the component-wise concave part of the functions, we consider an extended formulation of the convex envelope based on the Reformulation-Linearization-Technique introduced by Sherali and Adams(SIAM J Discret Math 3(3):411-430, 1990). Computational results are reported showing that the extended formulation strategy is a useful tool in global optimization

(Global) Optimization: Historical notes and recent developments

Recent developments in (Global) Optimization are surveyed in this paper. We collected and commented quite a large number of recent references which, in our opinion, well represent the vivacity, deepness, and width of scope of current computational approaches and theoretical results about nonconvex optimization problems. Before the presentation of the recent developments, which are subdivided into two parts related to heuristic and exact approaches, respectively, we briefly sketch the origin of the discipline and observe what, from the initial attempts, survived, what was not considered at all as well as a few approaches which have been recently rediscovered, mostly in connection with machine learning

Integrated Chemical Processes in Liquid Multiphase Systems

The essential principles of green chemistry are the use of renewable raw materials, highly efficient catalysts and green solvents linked with energy efficiency and process optimization in real-time. Experts from different fields show, how to examine all levels from the molecular elementary steps up to the design and operation of an entire plant for developing novel and efficient production processes

Extended formulations for convex envelopes

In this work we derive explicit descriptions for the convex envelope of nonlinear functions that are component-wise concave on a subset of the variables and convex on the other variables. These functions account for more than 30 % of all nonlinearities in common benchmark libraries. To overcome the combinatorial difficulties in deriving the convex envelope description given by the component-wise concave part of the functions, we consider an extended formulation of the convex envelope based on the Reformulation–Linearization-Technique introduced by Sherali and Adams (SIAM J Discret Math 3(3):411–430, 1990). Computational results are reported showing that the extended formulation strategy is a useful tool in global optimization.ISSN:0925-5001ISSN:1573-291