Related papers: Efficient Local and Tabu Search Strategies for Lar…
An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
Quadratic Unconstrained Binary Optimization (QUBO) is a general-purpose modeling framework for combinatorial optimization problems and is a requirement for quantum annealers. This paper utilizes the eigenvalue decomposition of the…
Mixed-Integer Programming (MIP), particularly Mixed-Integer Linear Programming (MILP) and Mixed-Integer Quadratic Programming (MIQP), has found extensive applications in domains such as portfolio optimization and network flow control, which…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…
Quadratically constrained quadratic programming (QCQP) has long been recognized as a computationally challenging problem, particularly in large-scale or high-dimensional settings where solving it directly becomes intractable. The complexity…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
The Tabu Search (TS) metaheuristic has been proposed for K-Means clustering as an alternative to Lloyd's algorithm, which for all its ease of implementation and fast runtime, has the major drawback of being trapped at local optima. While…
The Grover search algorithm performs an unstructured search of a marked item in a database quadratically faster than classical algorithms and is shown to be optimal. Here, we show that if the search space is divided into two blocks with the…
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
Local search algorithms use the neighborhood relations among search states and often perform well for a variety of NP-hard combinatorial search problems. This paper shows how quantum computers can also use these neighborhood relations. An…
This paper describes the development of an efficient algorithm for the optimization of fluid power circuits. The algorithm is based around the concepts of Tabu search, where different timescale memory cycles are used as a metaheuristic to…
Quadratic Unconstrained Binary Optimization (QUBO) is recognized as a unifying framework for modeling a wide range of problems. Problems can be solved with commercial solvers customized for solving QUBO and since QUBO have degree two, it is…