This study presents a novel Equiangular Direction Method (EDM) to solve a multi-objective optimization problem. We consider optimization problems, where multiple differentiable losses have to be minimized. The presented method computes descent direction in every iteration to guarantee equal relative decrease of objective functions. This descent direction is based on the normalized gradients of the individual losses. Therefore, it is appropriate to solve multi-objective optimization problems with multi-scale losses. We test the proposed method on the imbalanced classification problem and multi-task learning problem, where standard datasets are used. EDM is compared with other methods to solve these problems.
On solving integer bilevel optimization problems with a non-convex quadratic follower objective function using disjunctive cuts
Koç University（博阿兹奇大学）；University of Augsburg（奥格斯堡大学）；University of Michigan（密歇根大学）；Vienna University of Economics and Business（维也纳经济与商业大学）；Johannes Kepler University Linz（林茨约翰·开普勒大学）
Machine Learning-Augmented Optimization of Large Bilevel and Two-stage Stochastic Programs: Application to Cycling Network Design
Department of Mechanical & Industrial Engineering, University of Toronto（机械与工业工程系，多伦多大学）；Department of Civil & Mineral Engineering, University of Toronto（土木与矿物工程系，多伦多大学）
On the dynamic consistency of hierarchical risk-averse decision problems
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which there are two risk-averse decision makers (i.e., { \it leader} and { \it follower}) with different risk-averse related responsibilities and information. Moreover, we assume that there are two objectives that these decision makers are expected to achieve. That is, the first objective being of { \it stochastic controllability} type that describes an acceptable risk-exposure set vis-á-vis some uncertain future payoff, and while the { \it second one} is making sure the…
