Michael Muehlebach,Michael I Jordan
Michael Muehlebach
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected grad...
Fast convergence of trust-regions for non-isolated minima via analysis of CG on indefinite matrices [0.03%]
基于不定矩阵的共轭梯度分析的信赖域算法求非孤立极小点的快速收敛性研究
Quentin Rebjock,Nicolas Boumal
Quentin Rebjock
Trust-region methods (TR) can converge quadratically to minima where the Hessian is positive definite. However, if the minima are not isolated, then the Hessian there cannot be positive definite. The weaker Polyak-Łojasiewicz (PŁ) conditi...
Ahmad Abdi,Gérard Cornuéjols,Bertrand Guenin et al.
Ahmad Abdi et al.
A rational number is dyadic if it has a finite binary representation p / 2 k , where p is an integer and k is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in fl...
Benny Sudakov,István Tomon
Benny Sudakov
Given an m × n binary matrix M with | M | = p · m n (where |M| denotes the number of 1 entries), define the discrepancy of M as disc ( M ) = max X ⊂ [ m ] , Y ⊂ [ n ] | | M [ X × Y ] | - p | X | · | Y ...
Dirk Banholzer,Jörg Fliege,Ralf Werner
Dirk Banholzer
We present a novel response surface method for global optimisation of an expensive and noisy (black-box) objective function, where error bounds on the deviation of the observed noisy function values from their true counterparts are availabl...
Martin Nägele,Christian Nöbel,Richard Santiago et al.
Martin Nägele et al.
There has been significant work recently on integer programs (IPs) min { c ⊤ x : A x ≤ b , x ∈ Z n } with a constraint marix A with bounded subdeterminants. This is motivated by a well-known conjecture claiming that, for...
Constant-competitiveness for random assignment Matroid secretary without knowing the Matroid [0.03%]
不知道Matroid的随机分配恒定竞争力及.matroid秘书问题
Richard Santiago,Ivan Sergeev,Rico Zenklusen
Richard Santiago
The Matroid Secretary Conjecture is a notorious open problem in online optimization. It claims the existence of an O(1)-competitive algorithm for the Matroid Secretary Problem (MSP). Here, the elements of a weighted matroid appear one-by-on...
A linear time algorithm for linearizing quadratic and higher-order shortest path problems [0.03%]
线性时间算法用于线性化二次及更高阶的最短路径问题
Eranda Çela,Bettina Klinz,Stefan Lendl et al.
Eranda Çela et al.
An instance of the NP-hard Quadratic Shortest Path Problem (QSPP) is called linearizable iff it is equivalent to an instance of the classic Shortest Path Problem (SPP) on the same input digraph. The linearization problem for the QSPP (LinQS...
Daniel Dadush,Friedrich Eisenbrand,Thomas Rothvoss
Daniel Dadush
Approximate integer programming is the following: For a given convex body K ⊆ R n , either determine whether K ∩ Z n is empty, or find an integer point in the convex body 2 · ( K - c ) + c which is K, scaled by 2 from ...
Edin Husić,Zhuan Khye Koh,Georg Loho et al.
Edin Husić et al.
A set function can be extended to the unit cube in various ways; the correlation gap measures the ratio between two natural extensions. This quantity has been identified as the performance guarantee in a range of approximation algorithms an...