2021/12/07 by Jong‐Shi Pang, Pang, Jong-Shi, Shaoning Han +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2112.03886
openalex publication_date 2021/12/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with O(n3) strongly polynomial complexity, where n is the number of variables of the problem. Extension of the Hessian class is also discussed. Our research is motivated by a recent reference [7] wherein the efficient solution of a quadratic program with a tridiagonal Hessian matrix in the quadratic objective is needed for the construction of a polynomial-time algorithm for solving an associated sparse variable selection problem. With the tridiagonal structure, the complexity of the QP algorithm reduces to O(n2). Our strongly polynomiality results extend previous works of some strongly polynomially solvable linear complementarity problems with a P-matrix [9]; special cases of the extended results include weakly quasi-diagonally dominant problems in addition to the tridiagonal ones.