SIAM Journal on Optimization http://scitation.aip.org/ SIAM Journal on Optimization Duality of Ellipsoidal Approximations via Semi-Infinite Programming http://link.aip.org/link/?SJE/20/1421/1&agg=rss Filiz Gurtuna<br/> In this paper, we develop duality of the minimum volume circumscribed ellipsoid and the maximum volume inscribed ellipsoid problems. We present a unified treatment of both problems using convex semi-infinite programming. We establish the known duality relationship between the minimum volume circums ... [SIAM J. Optim. 20, 1421 (2009)] published Wed Nov 11, 2009. Version-Independence and Nested Distributions in Multistage Stochastic Optimization http://link.aip.org/link/?SJE/20/1406/1&agg=rss G. Ch. Pflug<br/> The amount of stagewise available information is crucial in multistage stochastic optimization. But unlike data, which directly enter the profit&loss functions of a decision problem, information is invariant w.r.t. bijective transformations. The usual concept to deal with information in multistage ... [SIAM J. Optim. 20, 1406 (2009)] published Wed Nov 11, 2009. Active Set Identification for Linearly Constrained Minimization Without Explicit Derivatives http://link.aip.org/link/?SJE/20/1378/1&agg=rss Robert Michael Lewis and Virginia Torczon<br/> We consider active set identification for linearly constrained optimization problems in the absence of explicit information about the derivative of the objective function. We begin by presenting some general results on active set identification that are not tied to any particular algorithm. These g ... [SIAM J. Optim. 20, 1378 (2009)] published Fri Oct 16, 2009. On the Complexity of Nonnegative Matrix Factorization http://link.aip.org/link/?SJE/20/1364/1&agg=rss Stephen A. Vavasis<br/> Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases, and other information retrieval and clustering applications. The problem is most naturally posed as continuous optimization. In this report, we define an exact version of NMF ... [SIAM J. Optim. 20, 1364 (2009)] published Fri Oct 16, 2009. On a Class of Superlinearly Convergent Polynomial Time Interior Point Methods for Sufficient LCP http://link.aip.org/link/?SJE/20/1333/1&agg=rss Florian A. Potra and Josef Stoer<br/> A new class of infeasible interior point methods for solving sufficient linear complementarity problems (LCPs) requiring one matrix factorization and $m$ backsolves at each iteration is proposed and analyzed. The algorithms from this class use a large $({\cal N}_\infty^-$) neighborhood of an infeas ... [SIAM J. Optim. 20, 1333 (2009)] published Fri Oct 16, 2009. Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations http://link.aip.org/link/?SJE/20/1286/1&agg=rss Chen Ling, Jiawang Nie, Liqun Qi, and Yinyu Ye<br/> This paper studies the so-called biquadratic optimization over unit spheres $\min_{x\in \mathbb{R}^n,y\in \mathbb{R}^m}\sum_{1\leq i,k\leq n,\,1\leq j,l \leq m}b_{ijkl}x_{i}y_{j}x_{k}{y}_l$, subject to $\|x\| = 1$, $\|y\| =1$. We show that this problem is NP-hard, and there is no polynomial time al ... [SIAM J. Optim. 20, 1286 (2009)] published Thu Oct 1, 2009. Single-Directional Property of Multivalued Maps and Variational Systems http://link.aip.org/link/?SJE/20/1274/1&agg=rss D. Aussel, Y. Garcia, and N. Hadjisavvas<br/> Dontchev and Hager [Math. Oper. Res., 19 (1994), pp. 753768] have shown that a monotone set-valued map defined from a Banach space to its dual which satisfies the Aubin property around a point $(x,y)$ of its graph is actually single-valued in a neighborhood of $x$. We prove a result which is the co ... [SIAM J. Optim. 20, 1274 (2009)] published Thu Oct 1, 2009. Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming http://link.aip.org/link/?SJE/20/1311/1&agg=rss D. H. Fang, C. Li, and K. F. Ng<br/> For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain ch ... [SIAM J. Optim. 20, 1311 (2009)] published Thu Oct 1, 2009. A Cutting-Surface Method for Uncertain Linear Programs with Polyhedral Stochastic Dominance Constraints http://link.aip.org/link/?SJE/20/1250/1&agg=rss Tito Homem-de-Mello and Sanjay Mehrotra<br/> In this paper we study linear optimization problems with a newly introduced concept of multidimensional polyhedral linear second-order stochastic dominance constraints. By using the polyhedral properties of this dominance condition, we present a cutting-surface algorithm and show its finite converg ... [SIAM J. Optim. 20, 1250 (2009)] published Thu Oct 1, 2009. A Matrix-Free Algorithm for Equality Constrained Optimization Problems with Rank-Deficient Jacobians http://link.aip.org/link/?SJE/20/1224/1&agg=rss Frank E. Curtis, Jorge Nocedal, and Andreas Wachter<br/> We present a line search algorithm for large-scale constrained optimization that is robust and efficient even for problems with (nearly) rank-deficient Jacobian matrices. The method is matrix-free (i.e., it does not require explicit storage or factorizations of derivative matrices), allows for inex ... [SIAM J. Optim. 20, 1224 (2009)] published Wed Sep 16, 2009.