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This paper is focused on the design of phase sequences with good (aperiodic) autocorrelation properties in terms of Peak Sidelobe Level (PSL) and Integrated Sidelobe Level (ISL). The problem is formulated as a bi-objective Pareto…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
An important challenge in multi-objective reinforcement learning is obtaining a Pareto front of policies to attain optimal performance under different preferences. We introduce Iterated Pareto Referent Optimisation (IPRO), which decomposes…
This paper investigates the privacy-preserving distributed optimization problem, aiming to protect agents' private information from potential attackers during the optimization process. Gradient tracking, an advanced technique for improving…
We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not…
We address the optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions. This type of Multi-Objective Distributional Optimization commonly arises in machine learning and…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
We consider the central role of improving directions in solution methods for mixed integer bilevel linear optimization problems (MIBLPs). Current state-of-the-art methods for solving MIBLPs employ the branch-and-cut framework originally…
In this paper, we study a first order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
We consider the problem of recovering off-the-grid spikes from linear measurements. The state of the art Over-Parametrized Continuous Orthogonal Matching Pursuit (OP-COMP) with Projected Gradient Descent (PGD) successfully recovers those…
Line-search methods are commonly used to solve optimization problems. The simplest line search method is steepest descent where one always moves in the direction of the negative gradient. Newton's method on the other hand is a second-order…
Multi-objective reinforcement learning (MORL) provides an effective solution for decision-making problems involving conflicting objectives. However, achieving high-quality approximations to the Pareto policy set remains challenging,…
This monograph presents a class of algorithms called coordinate descent algorithms for mathematicians, statisticians, and engineers outside the field of optimization. This particular class of algorithms has recently gained popularity due to…
The optimization of chemical processes is challenging due to the nonlinearities arising from process physics and discrete design decisions. In particular, optimal synthesis and design of chemical processes can be posed as a Generalized…
We present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier…
Decentralized methods to solve finite-sum minimization problems are important in many signal processing and machine learning tasks where the data is distributed over a network of nodes and raw data sharing is not permitted due to privacy…
In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…
Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to…
This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent…