Smoothing Approximation to the New Exact Penalty Function with Two Parameters

In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem. A global solution of the smoothed penalty problem is proved to be an approximation global solution of the non-smooth penalty problem. Based on the smoothed penalty function, we develop an algorithm and prove that the sequence generated by the algorithm can converge to the optimal solution of the original problem.

Constrained Linear Curvature Image Registration Model and Its Numerical Algorithm

We propose a constrained linear curvature image registration model to explicitly control the deformation according to the transformed Jacobian matrix determinant using point-by-point inequality constraints in this paper. In addition, an effective numerical method is proposed to solve the resulting inequality constrained optimization model. Finally, some numerical examples are given to prove the obvious advantages of the curvature image registration model with inequality constraints.

Coupling Elephant Herding with Ordinal Optimization for Solving the Stochastic Inequality Constrained Optimization Problems

The stochastic inequality constrained optimization problems (SICOPs) consider the problems of optimizing an objective function involving stochastic inequality constraints. The SICOPs belong to a category of NP-hard problems in terms of computational complexity. The ordinal optimization (OO) method offers an efficient framework for solving NP-hard problems. Even though the OO method is helpful to solve NP-hard problems, the stochastic inequality constraints will drastically reduce the efficiency and competitiveness. In this paper, a heuristic method coupling elephant herding optimization (EHO) with ordinal optimization (OO), abbreviated as EHOO, is presented to solve the SICOPs with large solution space. The EHOO approach has three parts, which are metamodel construction, diversification and intensification. First, the regularized minimal-energy tensor-product splines is adopted as a metamodel to approximately evaluate fitness of a solution. Next, an improved elephant herding optimization is developed to find N significant solutions from the entire solution space. Finally, an accelerated optimal computing budget allocation is utilized to select a superb solution from the N significant solutions. The EHOO approach is tested on a one-period multi-skill call center for minimizing the staffing cost, which is formulated as a SICOP. Simulation results obtained by the EHOO are compared with three optimization methods. Experimental results demonstrate that the EHOO approach obtains a superb solution of higher quality as well as a higher computational efficiency than three optimization methods.

Constrained Nonlinear Optimization in Information Science

This chapter provides an overview of constrained optimization methods. Background, theory, and examples are provided. Coverage includes Lagrange multipliers for equality constrained optimization with a Cobb-Douglass example from information science. The authors also provide Karush-Kuhn-Tucker for inequality-constrained optimization and a production example for smart phones with inequalities. An overview and discussion of numerical methods and techniques is also provided. The authors also provide a brief list of technology available to assist in solving these constrained nonlinear optimization problems.