Search · four archives
Search · four archives
12 papers · ranked by Valyu relevance
Fahaar Mansoor Pirani, Fırdevs Ulus
There is an existing exact algorithm that solves DC programming problems if one component of the DC function is polyhedral convex [16]. Motivated by this, first, we consider two cutting-plane algorithms for generating an ǫ-polyhedral underestimator of a convex function g. The algorithms start with a polyhedral…
Yuzhou Gu, Zhao Song, Lichen Zhang
Quadratic programming is a ubiquitous prototype in convex programming. Many combinatorial optimizations on graphs and machine learning problems can be formulated as quadratic programming; for example, Support Vector Machines (SVMs). Linear and kernel SVMs have been among the most popular models in machine learning over…
Kenneth Lange
The current paper proposes and tests algorithms for finding the diameter of a compact convex set and the farthest point in the set to another point. For these two nonconvex problems, I construct Frank-Wolfe and projected gradient ascent algorithms. Although these algorithms are guaranteed to go uphill, they can become…
Xinyi Luo, Andreas Wächter
We propose a new method for linear second-order cone programs. It is based on the sequential quadratic programming framework for nonlinear programming. In contrast to interior point methods, it can capitalize on the warm-start capabilities of active-set quadratic programming subproblem solvers and achieve a local…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Yichuan Deng, Zhao Song, Lichen Zhang, Ruizhe Zhang
Hyperbolic polynomials is a class of real-roots polynomials that has wide range of applications in theoretical computer science. Each hyperbolic polynomial also induces a hyperbolic cone that is of particular interest in optimization due to its generality, as by choosing the polynomial properly, one can easily recover…
Chen, Kaihuang, Sun, Defeng + 6 more
In this paper, we introduce HPR-QP, a dual Halpern Peaceman–Rachford (HPR) method designed for solving large-scale convex composite quadratic programming. One distinctive feature of HPR-QP is that, instead of working with the primal formulations, it builds on the novel restricted Wolfe dual introduced in recent years.…
Olga Brezhneva, Agnieszka Prusińska, Alexey A. Tret’yakov, Ravi P. Agarwal
'Ravi P. Agarwal'] The paper describes an application of the p-regularity theory to Quadratic Programming (QP) and nonlinear equations with quadratic mappings. In the first part of the paper, a special structure of the nonlinear equation and a construction of the 2-factor operator are used to obtain an exact formula…
Shaoze Li, Junhao Wu, Cheng Lü, Zhibin Deng + 1 more
Convex separable quadratic optimization problems occur in many practical applications. In this paper, based on an iterative resolution scheme of the KKT system, we develop an efficient method for solving a quadratic programming problem with a convex separable objective function subject to multiple convex separable…
Jamilu Sabi’u, Ado Balili, Homan Emadifar, Longxiu Huang
The Dai and Yuan conjugate gradient (CG) method is one of the classical CG algorithms using the numerator ‖g*k*+1‖2. When the usual Wolfe line search is used, the algorithm is shown to satisfy the descent condition and to converge globally when the Lipschitz condition is assumed. Despite these two advantages, the…
Kaitlin M. Stouffer, Alain Trouvé, Laurent Younes, Michael Kunst + 6 more
This paper explicates a solution to the problem of building correspondences between molecular-scale transcriptomics and tissue-scale atlases. The central model represents spatial transcriptomics as generalized functions encoding molecular position and high-dimensional transcriptomic-based (gene, cell type) identity. We…
Hao Hu, Renata Sotirov, Henry Wolkowicz
We consider both facial reduction, FR, and symmetry reduction, SR, techniques for semidefinite programming, SDP. We show that the two together fit surprisingly well in an alternating direction method of multipliers, ADMM, approach. In fact, this approach allows for simply adding on nonnegativity constraints, and…