| Generalized Pattern Search Algorithm is the main work in the paper. It is one of the direct search methods, and is usually applied to nonlinear optimization problems. The algorithm does not compute or approximate any derivatives, penalty constants, or Lagrange multipliers. Under the condition of not enforcing a notion of sufficient decrease, we can also obtain the convergence. Thus, it is widely applicable for nonlinear optimization problems.The analysis is possible because the iterates of the algorithm lie on a scaled,translated integer lattice, thus it can relax the classical requirements on the acceptance of the step, through placing stronger conditions on the form of the step, and still can maintain the convergence. The paper considers applying generalized pattern search methods to linear equality constrained minimization and analyzes the global convergence.The main results, obtained in this dissertation, may be summarized as follows:1. Chapter 1 states the original pattern search methods, the procedure of its development, and introduces the background of selecting this title and the main work in the paper.2. Chapter 2 gives the explicit description of generalized pattern search methods about unconstrained optimization and enumerates two kinds of search policies.3. Chapter 3 constructs a new generalized pattern search method for linear equality constrained optimization problems and gives the proofs of the global convergence. The method mainly adopts the projected gradient technique. Through calculating the fundus of the null space of matrix A in the constraint, the direction set becomes a positive spanning set of Rn-m. So at every nonstationary point there exists at least one feasible descent direction, every iterate generated by the methods is feasible so long as the initial iterate is feasible. Furthermore, the technique decreases the space dimension of the selected direction set from n to n — m, thus simplifying the implementation procedure and reducing the calculational cost. |
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