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Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…
Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and constraint functions. The algorithm is constructed by…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
Quadratic Unconstrained Binary Optimization (QUBO) is a combinatorial optimization to find an optimal binary solution vector that minimizes the energy value defined by a quadratic formula of binary variables in the vector. As many NP-hard…
A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…
Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model, and…
We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a nested double-loop structure, our framework features a…
We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic…
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical…
Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
Scaling the size of monolithic quantum computer systems is a difficult task. As the number of qubits within a device increases, a number of factors contribute to decreases in yield and performance. To meet this challenge, distributed…
There is an increasing interest in quantum algorithms for optimization problems. Within convex optimization, interior-point methods and other recently proposed quantum algorithms are non-trivial to implement on noisy quantum devices. Here,…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
We introduce a novel framework for implementing error-correction in constrained systems. The main idea of our scheme, called Quantized-Constraint Concatenation (QCC), is to employ a process of embedding the codewords of an error-correcting…
We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is…