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In this paper, a modified BFGS algorithm is proposed for unconstrained optimization. The proposed algorithm has the following properties: (i) a nonmonotone line search technique is used to obtain the step size $\alpha_{k}$ to improve the effectiveness of the algorithm; (ii) the algorithm possesses not only global convergence but also superlinear convergence for generally convex functions; (iii) the algorithm produces better numerical results than those of the normal BFGS method. [ABSTRACT FROM AUTHOR]

We present a family of new inexact secant methods in association with Armijo line search technique for solving nonconvex constrained optimization. Different from the existing inexact secant methods, the algorithms proposed in this paper need not compute exact directions. By adopting the nonsmooth exact penalty function as the merit function, the global convergence of the proposed algorithms is established under some reasonable conditions. Some numerical results indicate that the proposed algorithms are both feasible and effective. [ABSTRACT FROM AUTHOR]

In this paper, we present a flexible nonmonotone filter method for solving nonlinear constrained optimization problems which are common models in industry. This new method has more flexibility for the acceptance of the trial step compared to the traditional filter methods, and requires less computational costs compared with the monotone-type methods. Moreover, we use a self-adaptive parameter to adjust the acceptance criteria, so that Maratos effect can be avoided a certain degree. Under reasonable assumptions, the proposed algorithm is globally convergent. Numerical tests are presented that confirm the efficiency of the approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm for the solution of nonlinear constrained programming. This algorithm does not use any penalty function or a filter. Instead, it uses the idea of maximal constraint violation to guarantee global convergence. The infeasibility of each iterate is controlled by a progressively decreasing limit. At each iteration, a normal step which is obtained by solving a tightened normal subproblem and a tangential step which is a solution of a tangential subproblem are computed successively. The algorithm reduces the value of objective function or improves feasibility according to the relation of the tangential predicted reduction and the predicted reduction of constraint violation achieved by the trial step. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness of iterate sequence. Moreover, the algorithm does not need any restoration phase. We also include some preliminary yet promising numerical results on some standard test problems in constrained optimization. [ABSTRACT FROM AUTHOR]

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a new penalty-free-type method for nonlinear equality constrained problems. The new algorithm uses trust region framework and feasibility safeguarding technique. Moreover, it has no choice of penalty parameter and penalty function as a merit function, and it does not use the filter technique to avoid the penalty function either. We analyze the global convergence of the main algorithm under the standard assumptions. The preliminary numerical tests are reported. [Copyright &y& Elsevier]

Abstract: In this paper, an active set limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that the given method is effective. [Copyright &y& Elsevier]

Abstract: In this paper, we presented a modified QP-free filter method based on a new piecewise linear NCP functions. In contrast with the existing QP-free methods, each iteration in this algorithm only needs to solve systems of linear equations which are derived from the equality part in the KKT first order optimality conditions. Its global convergence and local superlinear convergence are obtained under mild conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a trust region method for unconstrained optimization that can be regarded as a combination of conic model, nonmonotone and line search techniques. Unlike in traditional trust region methods, the subproblem of our algorithm is the conic minimization subproblem; moreover, our algorithm performs a nonmonotone line search to find the next iteration point when a trial step is not accepted, instead of resolving the subproblem. The global and superlinear convergence results for the algorithm are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a nonmonotone trust region algorithm for unconstrained optimization problems is presented. In the algorithm, a kind of nonmonotone technique, which is evidently different from Grippo, Lampariello and Lucidi’s approach, is used. Under mild conditions, global and local convergence results of the algorithm are established. Preliminary numerical results show that the new algorithm is efficient. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new feasible primal–dual interior point algorithm for solving inequality constrained optimization problems is presented. At each iteration, the algorithm solves only two or three reduced systems of linear equations with the same coefficient matrix. The searching direction is feasible and the object function is monotone decreasing. The proposed algorithm is proved to possess global and superlinear convergence under mild conditions. Finally, some numerical experiments with the algorithm are reported. [Copyright &y& Elsevier]

Abstract: In last decades, there has been much effort on the solution and the analysis of the mixed complementarity problem (MCP) by reformulating MCP as an unconstrained minimization involving an MCP function. In this paper, we propose a new modified one-step smoothing Newton method for solving general (not necessarily ) mixed complementarity problems based on well-known Chen–Harker–Kanzow–Smale smooth function. Under suitable assumptions, global convergence and locally superlinear convergence of the algorithm are established. [Copyright &y& Elsevier]

Abstract: In this paper, by means of “working set” technique for determining the active set and the idea of primal–dual interior-point method, a new feasible QP-free algorithm for solving inequality constrained optimization problems is presented. At each iteration, the algorithm solves only three reduced systems of linear equations with common coefficient matrix. Moreover, the initial iteration point can be at constraint boundary and the coefficient matrix is uniformly nonsingular without the strict complementarity. We also prove that the proposed algorithm obtains global and superlinear convergence. At last, preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: In this paper, a modified SQP method is presented. The algorithm starts from an arbitrary initial point and can overcome the Maratos effect. Moreover, it avoid choosing the penalty parameters. Under some reasonable conditions, the global convergence is shown. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a QP-free type algorithm which solves the problem of minimizing a smooth function subject to smooth inequality constraints. In contrast with the SQP methods, each iteration this algorithm only needs to solve systems of linear equations which are derived from the equality part in the KKT first order optimality conditions. It is observed that, if the quasi-Newton direction is zero, we can obtain a direction of descent by dropping a constraint from the active set at the current iterate. A high order modified direction is introduced in order to prevent Maratos effect. Global and superlinear convergence are proven under some suitable conditions. [Copyright &y& Elsevier]