On direct sums and tensor products of non-linear programs

1965 ◽  
Vol 4 (1) ◽  
pp. 27-39 ◽  
Author(s):  
Bertram Mond
Keyword(s):  
Tensor Products ◽  
Linear Programs ◽  
Direct Sums ◽  
Non Linear

scholarly journals Bi-objective design-for-control of water distribution networks with global bounds

2021 ◽  
Author(s):  
Aly-Joy Ulusoy ◽  
Filippo Pecci ◽  
Ivan Stoianov
Keyword(s):  
Water Distribution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Mixed Integer ◽  
Global Optimality ◽  
Linear Programs ◽  
Design For Control ◽  
Non Linear ◽  
Feasible Solutions

AbstractThis manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of $$\epsilon $$ ϵ -constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

scholarly journals Norms on direct sums and tensor products

1972 ◽  
Vol 26 (118) ◽  
pp. 401-401 ◽  
Author(s):  
P. Lancaster ◽  
H. K. Farahat
Keyword(s):  
Tensor Products ◽  
Direct Sums

scholarly journals A symmetric dual theorem for non-linear programs

1965 ◽  
Vol 23 (3) ◽  
pp. 265-269 ◽  
Author(s):  
Bertram Mond
Keyword(s):  
Linear Programs ◽  
Dual Theorem ◽  
Non Linear
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