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**1 - 2**of**2**### A Framework for Parallel Nonlinear Optimization by Partitioning Localized Constraints ∗

"... We present a novel parallel framework for solving large-scale continuous nonlinear optimization problems based on constraint partitioning. The framework distributes constraints and variables to parallel processors and uses an existing solver to handle the partitioned subproblems. In contrast to most ..."

Abstract
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We present a novel parallel framework for solving large-scale continuous nonlinear optimization problems based on constraint partitioning. The framework distributes constraints and variables to parallel processors and uses an existing solver to handle the partitioned subproblems. In contrast to most previous decomposition methods that require either separability or convexity of constraints, our approach is based on a new constraint partitioning theory and can handle nonconvex problems with inseparable global constraints. We also propose a hypergraph partitioning method to recognize the problem structure. Experimental results show that the proposed parallel algorithm can efficiently solve some difficult test cases. 1

### Theory and Applications of Simulated Annealing for Nonlinear Constrained Optimization

"... A general mixed-integer nonlinear programming problem (MINLP) is formulated as follows: where z = (x, y) T ∈ Z; x ∈ Rv and y ∈ D w are, respectively, bounded continuous and discrete variables; f(z) is a lower-bounded objective function; g(z) = (g1(z),…, gr(z)) T is a vector of r inequality constrai ..."

Abstract
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A general mixed-integer nonlinear programming problem (MINLP) is formulated as follows: where z = (x, y) T ∈ Z; x ∈ Rv and y ∈ D w are, respectively, bounded continuous and discrete variables; f(z) is a lower-bounded objective function; g(z) = (g1(z),…, gr(z)) T is a vector of r inequality constraint functions; 2 and h(z) = (h1(z),…,hm(z)) T is a vector of m equality constraint