This paper presents a modification of the q-BFGS method for nonlinear unconstrained optimization problems. For this modification, we use simple symmetric positive definite matrix and propose new q-quasi-Newton equation, which is close to ordinary equation in limiting case. uses only first order q-derivatives build an approximate q-Hessian over number iterations. The q-Armijo-Wolfe line search c...

The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a Penal...

Nature inspired meta-heuristic algorithms are iterative search processes which find near optimal solutions by efficiently performing exploration and exploitation of the solution space. Considering the solution space in a specified region, this work compares performances of Bat, Cuckoo search and Firefly algorithms for unconstrained optimization problems. Global optima are found using various te...

In this paper, a modified conjugate gradient method is presented for solving large-scale unconstrained optimization problems, which possesses the sufficient descent property with Strong Wolfe-Powell line search. A global convergence result was proved when the (SWP) line search was used under some conditions. Computational results for a set consisting of 138 unconstrained optimization test probl...

The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical qubit network structure with specific size and edge density restrictions is generating a growing...

The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is...