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Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints

Journal Article · · SIAM Journal on Optimization
DOI:https://doi.org/10.1137/20m1370501· OSTI ID:1969125
 [1];  [2];  [2];  [3]
  1. Technische Univ. Braunschweig (Germany)
  2. Argonne National Lab. (ANL), Lemont, IL (United States)
  3. Argonne National Lab. (ANL), Lemont, IL (United States); Technische Univ. Dortmund (Germany)
+ Show Author Affiliations

Here, we propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate of the active set. The algorithm enforces descent on the objective function to promote global convergence to B-stationary points. We provide a convergence analysis and preliminary numerical results on a range of test problems. We also study the effect of fixing the active constraints in a bound-constrained quadratic program that can be solved on each iteration in order to obtain fast convergence.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Organization:
Deutsche Forschungsgemeinschaft (DFG); German Federal Ministry of Education and Research (BMBF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1969125
Journal Information:
SIAM Journal on Optimization, Journal Name: SIAM Journal on Optimization Journal Issue: 1 Vol. 32; ISSN 1052-6234
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

97 MATHEMATICS AND COMPUTING
B-stationarity
mathematical programs with complementarity constraints
sequential linear programming