Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints

1990 ◽  
Vol 48 (1-3) ◽  
pp. 265-284 ◽  
Author(s):  
Terry L. Friesz ◽  
Roger L. Tobin ◽  
Hsun-Jung Cho ◽  
Nihal J. Mehta
Keyword(s):  
Sensitivity Analysis ◽  
Variational Inequality ◽  
Heuristic Algorithms ◽  
Inequality Constraints ◽  
Mathematical Programs

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Nonlinear Programs ◽  
Mathematical Programs ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.

scholarly journals Lower bound for the cost of connecting tree with given vertex degree sequence

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Mikhail Goubko ◽  
Alexander Kuznetsov
Keyword(s):  
Lower Bound ◽  
Heuristic Algorithms ◽  
Degree Sequence ◽  
Real Life ◽  
Inequality Constraints ◽  
Topology Design ◽  
Semidefinite Optimization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
The Cost

Abstract The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, etc. For the case of connecting trees with the given sequence of vertex degrees the cost of the optimal tree is shown to be bounded from below by the solution of a semidefinite optimization program with bilinear matrix inequality constraints, which is reduced to the solution of a series of convex programs with linear matrix inequality constraints. The proposed lower-bound estimate is used to construct several heuristic algorithms and to evaluate their quality on a variety of generated and real-life datasets.

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