We introduce a quantum optimal control algorithm for energy minimization that combines the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) gradient and the Broyden Fletcher Goldfarb Shanno (BFGS) iterative scheme for nonlinear optimization. An extended set of controls defining the time-dependent mass, dipole moment, and external perturbational field are optimize...

We consider infinite-dimensional convex minimization problems with pointwise inequality constraints. We do not impose a constraint qualification condition, so that first-order necessary conditions are not available. To handle such problems we propose a method which combines advantages both from well-known penalty and barrier methods. For solving the resulting subproblems we develop a Newton-typ...

In this paper, a heuristic scheme is used to obtain the numerical solution of the non linear ordinary differential equations (NLODEs). The approximate solutions of the given NLODEs are deduced as a linear combination of some log sigmoid basis functions with unknown parameters. The given NLODEs are converted into equivalent global error minimization problems. Genetic algorithm (GA) and a hybrid ...

We extend pattern search methods to linearly constrained minimization. We develop a general class of feasible point pattern search algorithms and prove global convergence to a KarushKuhn-Tucker point. As in the case of unconstrained minimization, pattern search methods for linearly constrained problems accomplish this without explicit recourse to the gradient or the directional derivative of th...

Neural networks are usually trained using local, gradient-based procedures, and the best architectures are selected by experimentation. Gradient methods frequently find suboptimal solutions being trapped in local minima. Genetic algorithms are frequently used but do not guarantee optimal solutions and are computationally expensive. Several new global optimization methods suitable for architectu...

In this paper, we reformulate the stochastic generalized second-order cone complementarity problems as boxconstrained optimization problems. If satisfy the condition that the reformulation’s objective value is zero, the solutions of box-constrained optimization problems are also solutions of stochastic generalized second-order cone complementarity problems. Since the box-constrained minimizatio...

The iteratively reweighted `1 minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. However the convergence of the IRL1 has not been proved. In this paper, we prove that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the `2-`p minimization problem with 0 < p < 1. Moreover, the sta...

Many well-known machine learning and pattern recognition methods can be seen as special cases of sparse minimization of Positive Definite Quadratic Forms (PDQF). An algorithm framework of sparse minimization is proposed for PDQF. It is theoretically analyzed to converge to global minimum. The computational complexity is analyzed and compared with the state-of-the-art Fast Iterative ShrinkageThr...

The Karush-Kuhn-Tucker (KKT) conditions can be regarded as optimality conditions for both variational inequalities and constrained optimization problems. In order to overcome some drawbacks of recently proposed reformulations of KKT systems, we propose to cast KKT systems as a minimization problem with nonnegativity constraints on some of the variables. We prove that, under fairly mild assumpti...

This paper examines the problem of jobshop scheduling with either makespan minimization or total tardiness minimization, which are both known to be NP-hard. The authors propose the use of a meta-heuristic procedure inspired from bacterial phototaxis. This procedure, called Global Bacteria Optimization (GBO), emulates the reaction of some organisms (bacteria) to light stimulation. Computational ...