Related papers: A Second-Order Lower Bound for Globally Optimal 2D…
We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling problem. The high level…
The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems…
Bandit convex optimization (BCO) is a general framework for online decision making under uncertainty. While tight regret bounds for general convex losses have been established, existing algorithms achieving these bounds have prohibitive…
The problem of solving Markov decision processes under function approximation remains a fundamental challenge, even under linear function approximation settings. A key difficulty arises from a geometric mismatch: while the Bellman…
The Discrete Ordered Median Problem (DOMP) is formulated as a set partitioning problem using an exponential number of variables. Each variable corresponds to a set of demand points allocated to the same facility with the information of the…
We propose a machine learning enhanced algorithm for solving the optimal landing problem. Using Pontryagin's minimum principle, we derive a two-point boundary value problem for the landing problem. The proposed algorithm uses deep learning…
Finding global optima in high-dimensional optimization problems is extremely challenging since the number of function evaluations required to sufficiently explore the search space increases exponentially with its dimensionality.…
Recently two search algorithms, A* and breadth-first branch and bound (BFBnB), were developed based on a simple admissible heuristic for learning Bayesian network structures that optimize a scoring function. The heuristic represents a…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
We study binary optimization problems of the form \( \min_{x\in\{-1,1\}^n} f(Ax-b) \) with possibly nonsmooth loss \(f\). Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a…
The nonnegative rank of an entrywise nonnegative matrix A of size mxn is the smallest integer r such that A can be written as A=UV where U is mxr and V is rxn and U and V are both nonnegative. The nonnegative rank arises in different areas…
The sparse portfolio selection problem is one of the most famous and frequently-studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal…
Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…
Consensus-based optimization (CBO) is a versatile multi-particle optimization method for performing nonconvex and nonsmooth global optimizations in high dimensions. Proofs of global convergence in probability have been achieved for a broad…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
B* is a novel optimization framework that addresses a critical challenge in fixed-base manipulator robotics: optimal base placement. Current methods rely on pre-computed kinematics databases generated through sampling to search for…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
We address the problem of camera-to-laser-scanner calibration using a checkerboard and multiple image-laser scan pairs. Distinguishing which laser points measure the checkerboard and which lie on the background is essential to any such…
This paper propose a new frame work for finding global minima which we call optimization by cut. In each iteration, it takes some samples from the feasible region and evaluates the objective function at these points. Based on the…