An MPEC approach for the critical post-collapse behavior of rigid-plastic structures

Tangaramvong, Sawekchai; Tin‐Loi, F.; Senjuntichai, Teerapong

doi:10.1016/j.ijsolstr.2011.05.022

Cited by 4 publications

(1 citation statement)

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“…Complementarity, the requirement that at least one of a pair of variables be at some limit, provides a framework for representing disjunctive behavior using a set of continuous equations. MPECs using complementarity constraints have found use in optimization problems in the fields of structural mechanics [4,5], chemical and process engineering [6][7][8][9], electric power generation [10], climate change [11], traffic networks [12], operations research [13], economics [14], and other fields [15,16].…”

Section: Introductionmentioning

confidence: 99%

A Continuous Formulation for Logical Decisions in Differential Algebraic Systems using Mathematical Programs with Complementarity Constraints

et al. 2016

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This work presents a methodology to represent logical decisions in differential algebraic equation simulation and constrained optimization problems using a set of continuous algebraic equations. The formulations may be used when state variables trigger a change in process dynamics, and introduces a pseudo-binary decision variable, which is continuous, but should only have valid solutions at values of either zero or one within a finite time horizon. This formulation enables dynamic optimization problems with logical disjunctions to be solved by simultaneous solution methods without using methods such as mixed integer programming. Several case studies are given to illustrate the value of this methodology including nonlinear model predictive control of a chemical reactor using a surge tank with overflow to buffer disturbances in feed flow rate. Although this work contains novel methodologies for solving dynamic algebraic equation (DAE) constrained problems where the system may experience an abrupt change in dynamics that may otherwise require a conditional statement, there remain substantial limitations to this methodology, including a limited domain where problems may converge and the possibility for ill-conditioning. Although the problems presented use only continuous algebraic equations, the formulation has inherent non-smoothness. Hence, these problems must be solved with care and only in select circumstances, such as in simulation or situations when the solution is expected to be near the solver's initial point.

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