This paper works on a modified simplex algorithm for the local optimization of Continuous Piece Wise Linear（CPWL） programming with generalization of hinging hyperplane objective and linear constraints. CPWL programm...This paper works on a modified simplex algorithm for the local optimization of Continuous Piece Wise Linear（CPWL） programming with generalization of hinging hyperplane objective and linear constraints. CPWL programming is popular since it can be equivalently transformed into difference of convex functions programming or concave optimization. Inspired by the concavity of the concave CPWL functions, we propose an Objective Variation Simplex Algorithm（OVSA）, which is able to find a local optimum in a reasonable time. Computational results are presented for further insights into the performance of the OVSA compared with two other algorithms on random test problems.展开更多
In order to recover a signal from its compressive measurements, the compressed sensing theory seeks the sparsest signal that agrees with the measurements, which is actually an l;norm minimization problem. In this pape...In order to recover a signal from its compressive measurements, the compressed sensing theory seeks the sparsest signal that agrees with the measurements, which is actually an l;norm minimization problem. In this paper, we equivalently transform the l;norm minimization into a concave continuous piecewise linear programming,and propose an optimization algorithm based on a modified interior point method. Numerical experiments demonstrate that our algorithm improves the sufficient number of measurements, relaxes the restrictions of the sensing matrix to some extent, and performs robustly in the noisy scenarios.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 61473165 and 61134012)the National Key Basic Research and Development (973) Program of China (No. 2012CB720505)
文摘This paper works on a modified simplex algorithm for the local optimization of Continuous Piece Wise Linear（CPWL） programming with generalization of hinging hyperplane objective and linear constraints. CPWL programming is popular since it can be equivalently transformed into difference of convex functions programming or concave optimization. Inspired by the concavity of the concave CPWL functions, we propose an Objective Variation Simplex Algorithm（OVSA）, which is able to find a local optimum in a reasonable time. Computational results are presented for further insights into the performance of the OVSA compared with two other algorithms on random test problems.
基金supported by the National Natural Science Foundation of China(Nos.61473165 and 61134012)the National Key Basic Research and Development(973)Program of China(No.2012CB720505)
文摘In order to recover a signal from its compressive measurements, the compressed sensing theory seeks the sparsest signal that agrees with the measurements, which is actually an l;norm minimization problem. In this paper, we equivalently transform the l;norm minimization into a concave continuous piecewise linear programming,and propose an optimization algorithm based on a modified interior point method. Numerical experiments demonstrate that our algorithm improves the sufficient number of measurements, relaxes the restrictions of the sensing matrix to some extent, and performs robustly in the noisy scenarios.
