Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A polynomial-time algorithm for a class of linear complementary problems
Mathematical Programming: Series A and B
Efficient line search algorithm for unconstrained optimization
Journal of Optimization Theory and Applications
Interior algorithms for linear, quadratic, and linearly constrained convex programming
Interior algorithms for linear, quadratic, and linearly constrained convex programming
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
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A recent paper [14] has considered the possibility of combining interior point strategy with steepest descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, the paper [14] proposed a hybrid algorithm which combines a primal-dual potential reduction algorithm with the use of the steepest descent direction of the potential function. The O(√n|ln ε|) complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. In this paper, we discuss the relation between this method and general projected descent direction methods, and compare it with a projected steepest descent direction method for solving complex programming problems.