SIAM Journal on Optimization http://scitation.aip.org/ SIAM Journal on Optimization Projection-like Retractions on Matrix Manifolds http://link.aip.org/link/?SJE/22/135/1&agg=rss P.-A. Absil and Jerome Malick<br/> This paper deals with constructing retractions, a key step when applying optimization algorithms on matrix manifolds. For submanifolds of Euclidean spaces, we show that the operation consisting of taking a tangent step in the embedding Euclidean space followed by a projection onto the submanifold i ... [SIAM J. Optim. 22, 135 (2012)] published Thu Jan 26, 2012. On the Solution of the GPS Localization and Circle Fitting Problems http://link.aip.org/link/?SJE/22/108/1&agg=rss Amir Beck and Dror Pan<br/> We consider the problem of locating a user's position from a set of noisy pseudoranges to a group of satellites. We consider both the nonlinear least squares formulation of the problem, which is nonconvex and nonsmooth, and the nonlinear squared least squares variant, in which the objective functio ... [SIAM J. Optim. 22, 108 (2012)] published Thu Jan 26, 2012. Maximum Block Improvement and Polynomial Optimization http://link.aip.org/link/?SJE/22/87/1&agg=rss Bilian Chen, Simai He, Zhening Li, and Shuzhong Zhang<br/> In this paper we propose an efficient method for solving the spherically constrained homogeneous polynomial optimization problem. The new approach has the following three main ingredients. First, we establish a block coordinate descent type search method for nonlinear optimization, with the novelty ... [SIAM J. Optim. 22, 87 (2012)] published Tue Jan 24, 2012. On the Oracle Complexity of First-Order and Derivative-Free Algorithms for Smooth Nonconvex Minimization http://link.aip.org/link/?SJE/22/66/1&agg=rss Coralia Cartis, Nicholas I. M. Gould, and Philippe L. Toint<br/> The (optimal) function/gradient evaluations worst-case complexity analysis available for the adaptive regularization algorithms with cubics (ARC) for nonconvex smooth unconstrained optimization is extended to finite-difference versions of this algorithm, yielding complexity bounds for first-order a ... [SIAM J. Optim. 22, 66 (2012)] published Tue Jan 17, 2012. Perturbation Analysis of Error Bounds for Quasi-subsmooth Inequalities and Semi-infinite Constraint Systems http://link.aip.org/link/?SJE/22/41/1&agg=rss Xi Yin Zheng and Zhou Wei<br/> The stability of error bounds is significant in optimization theory and applications. Based on either the linearity assumption or the convexity and finite dimension assumption, several authors have focused on perturbation analysis of error bounds and obtained valuable results. Mainly motivated by N ... [SIAM J. Optim. 22, 41 (2012)] published Fri Jan 13, 2012. Fixed Points of Averages of Resolvents: Geometry and Algorithms http://link.aip.org/link/?SJE/22/24/1&agg=rss Heinz H. Bauschke, Xianfu Wang, and Calvin J. S. Wylie<br/> To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the early 19th century, when Carl Friedrich Gauss developed the method of least squares of a system of linear equationsits ... [SIAM J. Optim. 22, 24 (2012)] published Fri Jan 13, 2012. A Distance For Multistage Stochastic Optimization Models http://link.aip.org/link/?SJE/22/1/1&agg=rss Georg Ch. Pflug and Alois Pichler<br/> We describe multistage stochastic programs in a purely in-distribution setting, i.e., without any reference to a concrete probability space. The concept is based on the notion of nested distributions, which encompass in one mathematical object the scenario values as well as the information structur ... [SIAM J. Optim. 22, 1 (2012)] published Thu Jan 5, 2012. On the Evaluation Complexity of Composite Function Minimization with Applications to Nonconvex Nonlinear Programming http://link.aip.org/link/?SJE/21/1721/1&agg=rss Coralia Cartis, Nicholas I. M. Gould, and Philippe L. Toint<br/> We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it is unaffected by the nonsmoothness of the objective in that a first-order trust-region or quadratic regularizati ... [SIAM J. Optim. 21, 1721 (2011)] published Thu Dec 22, 2011. Complexity of Variants of Tseng's Modified F-B Splitting and Korpelevich's Methods for Hemivariational Inequalities with Applications to Saddle-point and Convex Optimization Problems http://link.aip.org/link/?SJE/21/1688/1&agg=rss Renato D. C. Monteiro and B. F. Svaiter<br/> In this paper, we consider both a variant of Tseng's modified forward-backward splitting method and an extension of Korpelevich's method for solving hemivariational inequalities with Lipschitz continuous operators. By showing that these methods are special cases of the hybrid proximal extragradient ... [SIAM J. Optim. 21, 1688 (2011)] published Thu Dec 22, 2011. Self-concordance and Decomposition-based Interior Point Methods for the Two-stage Stochastic Convex Optimization Problem http://link.aip.org/link/?SJE/21/1667/1&agg=rss Michael Chen and Sanjay Mehrotra<br/> We study the two-stage stochastic convex optimization problem whose first- and second-stage feasible regions admit a self-concordant barrier. We show that the barrier recourse functions and the composite barrier functions for this problem form self-concordant families. These results are used to dev ... [SIAM J. Optim. 21, 1667 (2011)] published Tue Dec 20, 2011.