SIAM Journal on Optimization

Let ${\cal S}$ denote the convex hull of $m$ full-dimensional ellipsoids in $\mathbb{R}^n$. Given $\epsilon > 0$ and $\delta > 0$, we study the problems of computing a $(1+ \epsilon)$-approximation to the minimum volume covering ellipsoid of ${\cal S}$ ...

The objectives of this paper are twofold. We devise a general framework for identifying locally optimal algorithmic parameters. Algorithmic parameters are treated as decision variables in a problem for which no derivative knowledge or existence is ...

We consider the problem of minimizing the number of bends in a planar orthogonal graph drawing. While the problem can be solved via network flow for a given planar embedding of a graph, it is NP-hard if we consider all planar embeddings. Our approach ...

This paper deals with approximate (&Vegr;-efficient) solutions of vector optimization problems. We introduce a new &Vegr;-efficiency concept which extends and unifies different approximate solution notions introduced in the literature. We obtain ...

The standard Schur complement equation-based implementation of interior-point methods for second order cone programming may encounter stability problems in the computation of search directions, and as a consequence, accurate approximate optimal ...

Today the vast majority of telecommunication and Internet messages are sent along fiber optic cables buried underground. Binary data (encoded as a sequence of pulses of light) may travel thousands of kilometers to reach its final destination. The fibers ...

An optimal control problem for a semilinear elliptic equation is investigated, where pointwise constraints are given on control and state. The state constraints are of mixed (bottleneck) type, where associated Lagrange multipliers can be chosen as ...

Recently, Huang and Ng presented second-order sufficient conditions for error bounds of continuous and Gaˆteaux differentiable functions in Banach spaces. Wu and Ye dropped the assumption of Huang and Ng on Gaˆteaux differentiability but required the ...

We show that any rational convex polytope is polynomial-time representable as a 3-way line-sum transportation polytope of “slim” $(r,c,3)$ format. This universality theorem has important consequences for linear and integer programming and for ...

We consider a polynomial programming problem $\P$ on a compact basic semialgebraic set $\K\subset\R^n$, described by $m$ polynomial inequalities $g_j(X)\geq0$, and with criterion $f\in\R[X]$. We propose a hierarchy of semidefinite relaxations in the ...

We consider the problem of minimizing an indefinite quadratic function subject to two quadratic inequality constraints. When the problem is defined over the complex plane we show that strong duality holds and obtain necessary and sufficient optimality ...

Using classes of sequentially pseudocontinuous functions, recently introduced by the authors, the aim of the paper is to investigate Tikhonov and parametric well-posedness for optimization problems when the objective functions are not necessarily ...

A higher order corrector-predictor interior-point method is proposed for solving sufficient linear complementarity problems. The algorithm produces a sequence of iterates in the $\caln_{\infty}^{-}$ neighborhood of the central path. The algorithm does ...

We investigate a class of two stage stochastic programs where the second stage problem is subject to nonsmooth equality constraints parameterized by the first stage variant and a random vector. We consider the case when the parametric equality ...

We consider the problem of computing the global infimum of a real polynomial $f$ on $\mathbb R^n$. Every global minimizer of $f$ lies on its gradient variety, i.e., the algebraic subset of $\mathbb R^n$ where the gradient of $f$ vanishes. If $f$ attains ...