Session: Relaxations for non-convex optimization
Chair: Andres Gomez
Cluster: Global Optimization
Talk 1: Convex Reformulations and Approximation Bounds for Low-Rank Semidefinite Programs
Speaker: Soroosh Shafiee
Abstract: Low-rank optimization has found numerous applications in finance, machine learning, and statistics. We develop convex relaxations for these problems in lifted spaces, leveraging perspective functions and majorization operators. These relaxations are shown to be provably stronger than existing approaches, such as those based on the nuclear norm. Additionally, we demonstrate that low-rank optimization problems in low-dimensional spaces typically exhibit a small duality gap, emphasizing the effectiveness and tightness of the relaxation
Talk 2: Multi-period mixed-integer quadratic programming
Speaker: Jisun Lee
Abstract: In this talk, we consider multi-period convex quadratic optimization problems with indicator variables, where the state linearly evolves from its current state subject to control inputs. This problem class has important applications in hybrid control and statistical learning. We give a compact convex hull description in an extended space with linear and conic quadratic inequalities for the uncapacited case. We also propose a polynomial-time algorithm. Computational experiments with data from neuron activation inference and hybrid-electric vehicle power management indicate promises and challenges.
Talk 3: TBD
Speaker: Chen Chen
Abstract: TBD
