Search · four archives
Search · four archives
12 papers · ranked by Valyu relevance
Kuang-Yu Ding, Xin-Yee Lam, Kim-Chuan Toh
We design inexact proximal augmented Lagrangian based decomposition methods for convex composite programming problems with dual block-angular structures. Our methods are particularly well suited for convex quadratic programming problems arising from stochastic programming models. The algorithmic framework is based on…
Kangkang Deng, Rui Wang, Zhenyuan Zhu, Junyu Zhang + 1 more
Large-scale constrained optimization is pivotal in modern scientific, engineering, and industrial computation, often involving complex systems with numerous variables and constraints. This paper provides a unified and comprehensive perspective on constructing augmented Lagrangian functions (based on…
Johannes Ø. Røyset
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large errors in the solutions. We specify conditions under which approximations are well…
Reza Rahimi Baghbadorani, Sergio Grammatico, Peyman Mohajerin Esfahani
'Peyman Mohajerin Esfahani'] Abstract. The choice of the stepsize in first-order convex optimization is typically based on the smoothness constant and plays a crucial role in the performance of algorithms. Recently, there has been a resurgent interest in introducing adaptive stepsizes that do not explicitly depend on…
You Yu, Yi-Shuai Niu
In this paper, we consider a composite difference-of-convex (DC) program, whose objective function is the sum of a smooth convex function with Lipschitz continuous gradient, a proper closed and convex function, and a continuous concave function. This problem has many applications in machine learning and data science.…
Philipp Schiele, Eric Luxenberg, Stephen Boyd
We consider convex-concave saddle point problems, and more generally convex optimization problems we refer to as saddle problems, which include the partial supremum or infimum of convex-concave saddle functions. Saddle problems arise in a wide range of applications, including game theory, machine learning, and finance.…
Gyeongcheol Cho, Heungsun Hwang
Generalized structured component analysis (GSCA) is a multivariate method for examining theory-driven relationships between variables including components. GSCA can provide the deterministic component score for each individual once model parameters are estimated. As the traditional GSCA always standardizes all…
Jan Kronqvist, Ruth Misener, Calvin Tsay
We develop a class of mixed-integer formulations for disjunctive constraints intermediate to the big-M and convex hull formulations in terms of relaxation strength. The main idea is to capture the best of both the big-M and convex hull formulations: a computationally light formulation with a tight relaxation. The…
Zhenwei Lin, Zikai Xiong, Dongdong Ge, Yinyu Ye
In this paper, we introduce the Primal-Dual Conic Programming Solver (PDCS), a largescale conic programming solver with GPU enhancements. Problems that PDCS currently supports include linear programs, second-order cone programs, convex quadratic programs, and exponential cone programs. PDCS achieves scalability to…
Richard D. Paul, Johann F. Jadebeck, Anton Stratmann, Wolfgang Wiechert + 1 more
Effective collaboration between developers of Bayesian inference methods and users is key to advance our quantitative understanding of biosystems. We here present hopsy, a versatile open source platform designed to provide convenient access to powerful Markov chain Monte Carlo sampling algorithms tailored to models…
Daniel Dadush, Friedrich Eisenbrand, Thomas Rothvoss
Approximate integer programming is the following: For a given convex body $K \subseteq{\mathbb{R}}^n$, either determine whether $K \cap{\mathbb{Z}}^n$ is empty, or find an integer point in the convex body $2\cdot K - c +c$ which is K, scaled by 2 from its center of gravity c. Approximate integer programming can be…
Mikhail A. Bragin, Emily L. Tucker
Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of integer decision variables, as the problem size increases, the number of possible…