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In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box.…
In this paper, we consider mixed-integer nonsmooth constrained optimization problems whose objective/constraint functions are available only as the output of a black-box zeroth-order oracle (i.e., an oracle that does not provide derivative…
We revisit first-order optimization under local information constraints such as local privacy, gradient quantization, and computational constraints limiting access to a few coordinates of the gradient. In this setting, the optimization…
In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…
We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
In the first part of this paper, we present a unified framework for analyzing the algorithmic complexity of any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like "input", "size" and…
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…
In bi-objective integer optimization the optimal result corresponds to a set of non-dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available…
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…
Distributed aggregative optimization underpins many cooperative optimization and multi-agent control systems, where each agent's objective function depends both on its local optimization variable and an aggregate of all agents' optimization…
In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
In this paper, we propose a Pre-trained Mixed Integer Optimization framework (PreMIO) that accelerates online mixed integer program (MIP) solving with offline datasets and machine learning models. Our method is based on a data-driven…
In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This…