We present a fixed point approach to find the whole solution set of a set-valued optimization problem though a parametric problem, in which the height of the level set of the objective function is regarded as the parameter. First, the solution concept based on the vector approach is considered in this method. Then, we propose … Read more
This article introduces a new retraction on the symplectic Stiefel manifold. The operation that requires the highest computational cost to compute the novel retraction is a matrix inversion of size $2p$–by–$2p$, which is much less expensive than those required for the available retractions in the literature. Later, with the new retraction, we design a constraint … Read more
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic structure of the proposed method is based on a step decomposition strategy that is known in the literature to be widely effective in practice, … Read more
We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. At each iteration, the function and the gradient are approximated by sampling. The sample size in gradient approximations is smaller than the sample size in function approximations and the latter is determined using a deterministic rule inspired … Read more
Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank-Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data Science and other relevant application areas. This review tries to explain the success of this approach by illustrating versatility … Read more
We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse application fields such as signal and image processing, portfolio selection, or machine learning. The paper discusses general-purpose modeling techniques and … Read more
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into this framework combine line searches and suitably decaying step lengths. A key issue is a two-step sampling at … Read more
The computational performance of inductive linearizations for binary quadratic programs in combination with a mixed-integer programming solver is investigated for several combinatorial optimization problems and established benchmark instances. Apparently, a few of these are solved to optimality for the first time. Citation preprint (no internal series / number): University of Bonn, Germany June 11, 2021 … Read more
MatQapNB is a MATLAB toolbox that implements a parallel branch-and-bound method using NewtBracket (the Newton bracketing method [4]) for its lower bounding procedure. It can solve small to medium scale Quadratic Assignment Problem (QAP) instances with dimension up to 30. MatQapNB was used in the numerical experiments on QAPs in the recent article “Solving challenging … Read more
In the application of data clustering to human-centric decision-making systems, such as loan applications and advertisement recommendations, the clustering outcome might discriminate against people across different demographic groups, leading to unfairness. A natural conflict occurs between the cost of clustering (in terms of distance to cluster centers) and the balance representation of all demographic groups … Read more