相关论文: Optimal frame designs for multitasking devices wit…

A fundamental challenge in the design of photonic devices, and electromagnetic structures more generally, is the optimization of their overall architecture to achieve a desired response. To this end, topology or shape optimizers based on…

Motivated by the cloud computing paradigm, and by key optimization problems in all-optical networks, we study two variants of the classic job interval scheduling problem, where a reusable resource is allocated to competing job intervals in…

We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently…

In this paper we present new constructive methods, random and deterministic, for the efficient subsampling of finite frames in $\mathbb C^m$. Based on a suitable random subsampling strategy, we are able to extract from any given frame with…

Let $F \in \mathbb{Z}[x_0, \ldots, x_n]$ be homogeneous of degree $d$ and assume that $F$ is not a `nullform', i.e., there is an invariant $I$ of forms of degree $d$ in $n+1$ variables such that $I(F) \neq 0$. Equivalently, $F$ is…

We address the problem of minimizing a smooth function $f^0(x)$ over a compact set $D$ defined by smooth functional constraints $f^i(x)\leq 0,~ i = 1,\ldots, m$ given noisy value measurements of $f^i(x)$. This problem arises in…

Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…

The celebrated Johnson-Lindenstrauss lemma states that for all $\varepsilon \in (0,1)$ and finite sets $X \subseteq \mathbb{R}^N$ with $n>1$ elements, there exists a matrix $\Phi \in \mathbb{R}^{m \times N}$ with…

We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and…

We survey incremental methods for minimizing a sum $\sum_{i=1}^mf_i(x)$ consisting of a large number of convex component functions $f_i$. Our methods consist of iterations applied to single components, and have proved very effective in…

Given $d, N\geq 2$ and $p\in (0, \infty]$ we consider a family of functionals, the $p$-frame potentials FP$_{p, N, d}$, defined on the set of all collections of $N$ unit-norm vectors in $\mathbb R^d$. For the special case $p=2$ and…

In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…

We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…

In this paper, we focus on the following general shape optimization problem: $$ \min\{J(\Om), \Om convex, \Om\in\mathcal S_{ad}\}, $$ where $\mathcal S_{ad}$ is a set of 2-dimensional admissible shapes and $J:\mathcal{S}_{ad}\to\R$ is a…

We propose a novel decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising naturally in the system design of wireless multiuser interfering systems. Our main contributions are: i) the…

Let $\D_{v,b,k}$ denote the family of all connected block designs with $v$ treatments and $b$ blocks of size $k$. Let $d\in\D_{v,b,k}$. The replication of a treatment is the number of times it appears in the blocks of $d$. The matrix…

When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…

In this paper, the filter-and-forward (FF) relay design for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems is considered. Due to the considered MIMO structure, the problem of joint design of…