The tensor method for unconstrained optimization was first introduced by Schnable and Chow [SIAM Journal on Optimization, 1 (1991): 293–315], where each iteration bases upon a fourth order model for the objective function. In this paper, we propose a tensor method with a non-monotone line search scheme for solving the unconstrained optimization problem, and show the convergence of the method. W...

This paper considers the problem of minimizing a frequency-weighted l2-sensitivity measure subject to l2scaling constraints for 2-D state-space digital filters. First, the frequency-weighted l2-sensitivity is analyzed for 2-D state-space digital filters described by the Roesser local state-space model. Next, the minimization problem of the frequency-weighted l2-sensitivity subject to l2-scaling...

Abstract Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, problems need to be formulated as unconstrained binary models, taking into account limitation and advantages of devices. In this work, we provide detailed analysis travelling salesman problem with time windows (TSPTW) in con...

In the field of global optimization many efforts have been devoted to solve unconstrained global optimization problems. The aim of this paper is to show that unconstrained global optimization methods can be used also for solving constrained optimization problems, by resorting to an exact penalty approach. In particular, we make use of a nondifferentiable exact penalty function Pq(x; ε). We show...

This paper is devoted to constructing a definite efficient scheme for non-smooth optimization. A separating plane algorithm with additional clipping is proposed. The algorithm is used for solving the unconstrained non-smooth convex optimization problem. The latter problem can be reformulated as the computation of the value of a conjugate function at the origin. The algorithm convergence is prov...

This paper introduces the variable objective search framework for combinatorial optimization. The method utilizes different objective functions used in alternative mathematical programming formulations of the same combinatorial optimization problem in an attempt to improve the solutions obtained using each of these formulations individually. The proposed technique is illustrated using alternati...

A quantum annealer heuristically minimizes quadratic unconstrained binary optimization (QUBO) problems, but is limited by the physical hardware in the size and density of the problems it can handle. We have developed a meta-heuristic solver that utilizes D-Wave Systems’ quantum annealer (or any other QUBO problem optimizer) to solve larger or denser problems, by iteratively solving subproblems,...

Finding the best weights of the state variables and the control variables in the objective function of a linear-quadratic control problem is considered. The weights of these variables are considered as two diagonal matrices with appropriate size and so the objective function of the control problem becomes a function of the diagonal elements of these matrices. The optimization problem which is d...

Consider the single-facility Euclidean κ-centrum location problem in R. This problem is a generalization of the classical Euclidean 1-median problem and 1-center problem. In this paper, we develop two efficient algorithms that are particularly suitable for problems where n is large by using unconstrained optimization techniques. The first algorithm is based on the neural networks smooth approxi...