The SDPA (SemiDefinite Programming Algorithm) Project launched in 1995 has been known to provide high-performance packages for solving large-scale Semidefinite Programs (SDPs). SDPA Ver. 6 solves efficiently large-scale dense SDPs, however, it required much computation time compared with other software packages, especially when the Schur complement matrix is sparse. SDPA Ver. 7 is now completely … Read more
In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. We propose primal-dual interior point methods based on the unscaled and scaled Newton methods, which correspond to the AHO, HRVW/KSH/M and NT search directions in linear SDP problems. We analyze local behavior of our proposed methods and show their … Read more
We present a primal-dual interior point method for constrained nonlinear, discrete minimax problems where the objective functions and constraints are not necessarily convex. The algorithm uses two merit functions to ensure progress towards the points satisfying the first order optimality conditions of the original problem. Convergence properties are described and numerical results provided. CitationDept. of … Read more
In this paper we develop several polynomial-time interior-point methods (IPM) for solving nonlinear primal-dual conic optimization problem. We assume that the barriers for the primal and the dual cone are not conjugate. This broken symmetry does not allow to apply the standard primal-dual IPM. However, we show that in this situation it is also possible … Read more
We propose an adaptive, constraint-reduced, primal-dual interior-point algorithm for convex quadratic programming with many more inequality constraints than variables. We reduce the computational e ort by assembling, instead of the exact normal-equation matrix, an approximate matrix from a well chosen index set which includes indices of constraints that seem to be most critical. Starting with a … Read more
A support vector machine (SVM) determines whether a given observed pattern lies in a particular class. The decision is based on prior training of the SVM on a set of patterns with known classification, and training is achieved by solving a convex quadratic programming problem. Since there are typically a large number of training patterns, … Read more
We consider the problem of adjusting speeds of multiple computer processors sharing the same thermal environment, such as a chip or multi-chip package. We assume that the speed of processor (and associated variables, such as power supply voltage) can be controlled, and we model the dissipated power of a processor as a positive and strictly … Read more
In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed within the framework of the line search strategy. We show the global convergence property of our method. Finally some numerical … Read more
We present a null-space primal-dual interior-point algorithm for solving nonlinear optimization problems with general inequality and equality constraints. The algorithm approximately solves a sequence of equality constrained barrier subproblems by computing a predictor step and a null space step in every iteration. The $\ell_2$ penalty function is taken as the merit function. Under very mild … Read more
Exploiting sparsity has been a key issue in solving large-scale optimization problems. The most time-consuming part of primal-dual interior-point methods for linear programs, second-order cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of the coefficient … Read more