The second-order cone programming problem is reformulated into several new systems of nonlinear equations. Assume the perturbation of the data is in a certain neighborhood of zero. Then starting from a solution to the old problem, the semismooth Newton’s iterates converge Q-quadratically to a solution of the perturbed problem. The algorithm is globalized. Numerical examples … Read more
There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of epsilon-optimal solutions, and (ii) the maximum distance of epsilon-optimal solutions to the … Read more
Test problems are generally used to effectively evaluate the algorithms for packing problem. Based on the engineering background of the layout optimization for a retrievable satellite module, this paper describes the test problems for circles packing problem with known optimization solution first. There are N(≦217) circular objects, different in size, packed in a circular container … Read more
This paper studies a new primal-dual interior/exterior-point method for linear programming. We begin with the usual perturbed primal-dual optimality equations $F_\mu(x,y,z)=0$. Under nondegeneracy assumptions, this nonlinear system is well-posed, i.e. it has a nonsingular Jacobian at optimality and is not necessarily ill-conditioned as the iterates approach optimality. We use a simple preprocessing step to eliminate … Read more
The main focus of this paper is discussion of complexity of stochastic programming problems. We argue that two-stage (linear) stochastic programming problems with recourse can be solved with a reasonable accuracy by using Monte Carlo sampling techniques, while multi-stage stochastic programs, in general, are intractable. We also discuss complexity of chance constrained problems and multi-stage … Read more
A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version … Read more
The conjugate gradient (CG) algorithm is well-known to have excellent theoretical properties for solving linear systems of equations $Ax = b$ where the $n\times n$ matrix $A$ is symmetric positive definite. However, for extremely ill-conditioned matrices the CG algorithm performs poorly in practice. In this paper, we discuss an adaptive preconditioning procedure which improves the … Read more
One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm, while misclassification means lying on the wrong side of the hyperplane, … Read more
One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm,while misclassification means lying on the wrong side of the hyperplane, or … Read more
We present a new complexity result on solving the Markov decision problem (MDP) with $n$ states and a number of actions for each state, a special class of real-number linear programs with the Leontief matrix structure. We prove that, when the discount factor $\theta$ is strictly less than $1$, the problem can be solved in … Read more