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On minimization of a quadratic function with one negative eigenvalue

... suggest to make a single partition of the feasible set in a concave variable only so that a convex approximation of the objective function upon every partition set has an acceptable error. Minimizing convex approximations on partition sets provides an approximate solution of the nonconvex quadratic program that we consider. These minimization problems are to be solved concurrently by parallel computing. An estimation of the number of partition sets is given. The study presents a computational comparison ...

Теги: branch-and-bound method , global optimization , parallel computing , quadratic programming , np-hard , approximate solution , computational comparisons , convex approximation , minimization problems , nonconvex quadratic programs , objective functions , partition se
Interior point and newton methods in solving high dimensional flow distribution problems for pipe networks

... flow distribution problem in pipe network is considered. The investigated problem is a convex sparse optimization problem with linear equality and inequality constrains. Newton method is used for problem with equality constrains only and obtains an approximate solution, which may not satisfy inequality constraints. Then Dikin Interior Point Method starts from the approximate solution and finds an optimal one. For problems of high dimension sparse matrix methods, namely Conjugate Gradient and Cholesky ...

Теги: convex optimization , interior point method , large-scale optimization , newton method , pipe network , sparse matrix , constraint theory , linear programming , newton-raphson method , optimization , quadratic programming , approximate solution , inequality constrain


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