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In this study, we apply 1D quantum convolution to address the task of time series forecasting. By encoding multiple points into the quantum circuit to predict subsequent data, each point becomes a feature, transforming the problem into a…
This paper presents a scalable method for improving the solutions of AC Optimal Power Flow (AC OPF) with respect to deviations in predicted power injections from wind and other uncertain generation resources. The focus of the paper is on…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex…
"Weakly coupled dynamic program" describes a broad class of stochastic optimization problems in which multiple controlled stochastic processes evolve independently but subject to a set of linking constraints imposed on the controls. One…
Many algorithms in verification and automated reasoning leverage some form of duality between proofs and refutations or counterexamples. In most cases, duality is only used as an intuition that helps in understanding the algorithms and is…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the…
In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the…
Quantum computing has been regarded as a promising approach to accelerate power system optimization. However, challenges such as limited qubits and inherent noise hinder their widespread adoption in power systems. In this paper, we propose…
Quantum machine learning is arguably one of the most explored applications of near-term quantum devices. Much focus has been put on notions of variational quantum machine learning where parameterized quantum circuits (PQCs) are used as…
The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized…
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
When compared to fault-tolerant quantum computational strategies, variational quantum algorithms stand as one of the candidates with the potential of achieving quantum advantage for real-world applications in the near term. However, the…
Most numerical methods for conic problems use the homogenous primal-dual embedding, which yields a primal-dual solution or a certificate establishing primal or dual infeasibility. Following Patrinos (and others, 2018), we express the…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
Sparse and convolutional constraints form a natural prior for many optimization problems that arise from physical processes. Detecting motifs in speech and musical passages, super-resolving images, compressing videos, and reconstructing…
Second-order cone programs (SOCPs) with quadratic objective functions are common in optimal control and other fields. Most SOCP solvers which use interior-point methods are designed for linear objectives and convert quadratic objectives…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…