How to alleviate the sensitivity of active contour models to their initial curves and how to keep convergent to the global minimum during the iterative procedure of energy minimization are difficult problems for solving the active contour models.
A new hybrid interval partical swarm optimization is presented in this parper. The arithmetic includes two parts. Firstly,we apply interval arithmetic to delete a majority of search space which don't include global minimum.
3. KKT second order sufficiency condition of the primal constrained nonlinear programming problem holds at its any global minimum, we establish the global exact penalty property, i.e. the set of global minima of the primal constrained nonlinear programming problem is identical to the set of global minima of the l1 exact penalty problem.
The spectral-estimation matrix is formed from the projection matrix to estimate the direction of arrival and unknown error's parameters simultaneously,and the simulation annealing is utilized to guarantee that algorithm converges to the global minimum.
One point of the initial multi-form is replaced with the local minimum gotten by the new ant colony algorithm using the substitution rule based on the minimum hamming distance and the complex method is apt to find the global minimum safety factor.
Utilizing the equivalent Problem(Q) of problem(P) and linearization technique,relaxed linear programming(RLP) about problem(Q) is established,through the successive refinement of the linear relaxation of the feasible region of the objection function and the solutions of a series of(RLP),and from theory the proof which the proposed algorithm is convergent to the global minimum is gived.
By utilizing the equivalent Problem(Q) of problem(P) and linear relaxation technique,a relaxation linear programming(RLP) problem about problem(P) is established,through the successive refinement of the linear relaxation of the feasible region of the objection function and the solutions of a series of relaxation linear programming(RLP),and from theory the proof which the proposed branch and bound algorithm is convergent to the global minimum is gived.
Based on the merit of computing global minimum with homotopy continuation method in , a posterior regularized homotopy continuation method is presented in this thesis. Regularized parameter in the iteration is decided by Morozov discrepancy principle.
Some new properties of(F,ρ)-invexity functions on the basis of the former researches are discussed,some of the established conclusion are expanded. A sufficient condition to verify the unique ness of global minimum about function f(x) is gotten.
The unconstrained optimization mathematical model is established for assessing roundness errors by the minimum zone method with the radial measurement approach. The properties of the objective function concerned are thoroughly researched into. On the basis of the modern theory on the convex function,it is strictly proved that the established roundness objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space R2.Therefore,the global minimum value of the objective function is unique.