Every multistage stochastic programming problem with recourse (MSPR) contains a filtration process. In this research, we created a notation that makes the filtration process the central syntactic construction of the MSPR. As a result, we achieve lower redundancy and higher modularity than is possible with the mathematical notation commonly associated with stochastic programming. To experiment … Read more
The NEOS Server provides access to a variety of optimization resources via the Internet. The new Kestrel interface to the Server enables local modeling environments to request NEOS optimization services and retrieve the results for local visualization and analysis, so that users have the same convenient access to remote NEOS solvers as to those installed … Read more
In this paper we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove … Read more
It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski [2] increases the numerical complexity of the solution compared to the original problem. Kocvara, Nemirovski and Zowe therefore introduced in [9] an approximation algorithm for the special case of robust material optimization, called cascading. As the title already indicates, we will show … Read more
We provide a sufficient condition on a class of compact basic semialgebraic sets K for their convex hull to have a lifted semidefinite representation (SDr). This lifted SDr is explicitly expressed in terms of the polynomials that define K. Examples are provided. For convex and compact basic semi-algebraic sets K defined by concave polynomials, we … Read more
One of the main drawbacks associated with Interior Point Methods (IPM) is the perceived lack of an efficient warmstarting scheme which would enable the use of information from a previous solution of a similar problem. Recently there has been renewed interest in the subject. A common problem with warmstarting for IPM is that an advanced … Read more
VSDP is a MATLAB software package for rigorously solving semidefinite programming problems. It expresses these problems in a notation closely related to the form given in textbooks and scientific papers. Functions for computing verified forward error bounds of the true optimal value and verified certificates of feasibility and infeasibility are provided. All rounding errors due … Read more
In this paper, we give a recursive formula for optimal dual barrier functions on homogeneous cones. This is done in a way similar to the primal construction of Guler and Tuncel by means of the dual Siegel cone construction of Rothaus. We use invariance of the primal barrier function with respect to a transitive subgroup … Read more
We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM, completion problem and to show the advantages for using this latter, well studied model. We first show that the current … Read more
In this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular graphs. Our technique involves semidefinite programming and exploiting the algebra structure of the optimization problem … Read more