相关论文: A Subgradient Approach for Constrained Binary Opti…
Quantum adiabatic evolution is perceived as useful for binary quadratic programming problems that are a priori unconstrained. For constrained problems, it is a common practice to relax linear equality constraints as penalty terms in the…
We propose an approach to solving constrained combinatorial optimization problems based on embedding the concept of Lagrangian duality into the framework of adiabatic quantum computation. Within the setting of circuit-model fault-tolerant…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Recent advances in the development of commercial quantum annealers such as the D-Wave 2X allow solving NP-hard optimization problems that can be expressed as quadratic unconstrained binary programs. However, the relatively small number of…
We propose a new method for solving binary optimization problems under inequality constraints using a quantum annealer. To deal with inequality constraints, we often use slack variables, as in previous approaches. When we use slack…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
The standard approach to encoding constraints in quantum optimization is the quadratic penalty method. Quadratic penalties introduce additional couplings and energy scales, which can be detrimental to the performance of a quantum optimizer.…
This paper describes how to make the problem of binary classification amenable to quantum computing. A formulation is employed in which the binary classifier is constructed as a thresholded linear superposition of a set of weak classifiers.…
Adiabatic quantum computing is implemented on specialized hardware using the heuristics of the quantum annealing algorithm. This setup requires the addressed problems to be formatted as discrete quadratic functions without constraints and…
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a…
Solving optimization problems on quantum annealers usually requires each variable of the problem to be represented by a connected set of qubits called a logical qubit or a chain. Chain weights, in the form of ferromagnetic coupling between…
This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes…
Quantum annealing may provide advantages over simulated annealing on solving some problems such as Kth order binary optimization problem. No feasible architecture exists to implement the high-order optimization problem (K > 2) on current…
Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…