Related papers: Inner approximation algorithm for solving linear m…
In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different from it, the…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
Real-world problems often involve the optimization of several objectives under multiple constraints. An example is the hyper-parameter tuning problem of machine learning algorithms. In particular, the minimization of the estimation of the…
In decision-making systems, algorithmic recourse aims to identify minimal-cost actions to alter an individual features, thereby obtaining a desired outcome. This empowers individuals to understand, question, or alter decisions that…
Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We present a new inverse optimization methodology for multi-objective convex optimization that accommodates an input solution that may not be Pareto optimal and determines a weight vector that produces a Pareto optimal solution that…
A common goal in evolutionary multi-objective optimization is to find suitable finite-size approximations of the Pareto front of a given multi-objective optimization problem. While many multi-objective evolutionary algorithms have proven to…
Second-order Newton-type algorithms that leverage the exact Hessian or its approximation are central to solve nonlinear optimization problems. However, their applications in solving large-scale nonconvex problems are hindered by three…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
In engineering optimization problems, multiple objectives with a large number of variables under highly nonlinear constraints are usually required to be simultaneously optimized. Significant computing effort are required to find the Pareto…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…