## The Theory And Applications Of Discrete Constrained Optimization Using Lagrange Multipliers (2000)

Citations: | 4 - 0 self |

### BibTeX

@TECHREPORT{Wu00thetheory,

author = {Zhe Wu},

title = {The Theory And Applications Of Discrete Constrained Optimization Using Lagrange Multipliers},

institution = {},

year = {2000}

}

### OpenURL

### Abstract

In this thesis, we present a new theory of discrete constrained optimization using Lagrange multipliers and an associated first-order search procedure (DLM) to solve general constrained optimization problems in discrete, continuous and mixed-integer space. The constrained problems are general in the sense that they do not assume the differentiability or convexity of functions. Our proposed theory and methods are targeted at discrete problems and can be extended to continuous and mixed-integer problems by coding continuous variables using a floating-point representation (discretization). We have characterized the errors incurred due to such discretization and have proved that there exists upper bounds on the errors. Hence, continuous and mixed-integer constrained problems, as well as discrete ones, can be handled by DLM in a unified way with bounded errors.

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Citation Context ...ly, we compare our algorithms to Grasp [130], one of the best complete algorithms. Since Grasp performs the best on most DIMACS benchmarks [130] when compared to other complete methods, such as POSIT =-=[62]-=-, CSAT [49], H2R [152] and DPL---a recent implementation of the Davis-Putnam procedure [14], we compare our results with respect to Grasp only. Since Grasp is a complete method that can prove unsatisf... |

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Citation Context ...cision formulations , defined in (6.1), entail the search of solutions that can satisfy all the clauses. Existing methods in this class are generally complete 147 methods. Examples include resolution =-=[14, 157, 68, 45]-=-, backtracking [154], and consistency testing [84, 89]. Due to the exhaustive nature of these search methods, they are expensive to use and normally have di#culty to address large-size problems. There... |

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Citation Context ...re a solution is represented by a string of binary bits (00011010010 for example). However, for many real-world problems, it is di#cult and ine#cient to use a binary representation. It has been found =-=[54]-=- that real-number encoding performs better than binary or Gray encoding for function and constraint optimization. The reason is that the topological structure of the coding space for a real-number enc... |

105 |
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Citation Context ... methods may be trapped by local minima in the objective space, various global-search strategies have been proposed. Next, we discuss briefly some existing methods using unconstrained formulations Gu =-=[87, 190, 86, 85]-=- proposed a number of local search and parallel local search for solving SAT problems. The various strategies proposed include iterative perturbation of trajectories and randomized search for overcomi... |