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In this paper we discuss the polynomiality of a feasible version of Mehrotra's predictor-corrector algorithm whose variants have been widely used in several interior point method (IPM)-based optimization packages. A numerical example is given that shows that the adaptive choice of centering parameter and correction terms in this algorithm may lead to small steps being taken in order to keep the iterates in a large neighborhood of the central path, which is important for proving polynomial complexity properties of this method. Motivated by this example, we introduce a safeguard in Mehrotra's algorithm that keeps the iterates in the prescribed neighborhood and allows us to obtain a positive lower bound on the step size. This safeguard strategy is also used when the affine scaling direction performs poorly. We prove that the safeguarded algorithm will terminate after at most O(n2log(x°}T s° /e) iterations. By modestly modifying the corrector direction, we reduce the iteration complexity to O(nlog(x°}T s° /e). To ensure fast asymptotic convergence of the algorithm, we changed Mehrotra's updating scheme of the centering parameter slightly while keeping the safeguard. The new algorithms have the same order of iteration complexity as the safeguarded algorithms but enjoy superlinear convergence as well. Numerical results using the McIPM and LIPSOL software packages are reported. [ABSTRACT FROM AUTHOR]

In this paper, a mixed QP-free method for constrained optimization problem is proposed. This new method consists of two different sub-methods, sub-method I and sub-method II. These two sub-methods are all QP-free. A switch is designed to decide which sub-method should be adopted in each iteration. Under some mild assumptions, we prove that the method is globally and superlinearly convergent. [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]

Evolutionary Algorithms (EA) have been successfully employed for solving difficult constrained engineering optimization problems. However, EA implementations often suffer from premature convergence due to the lack of proper balance between exploration and exploitation in the search process. This paper proposes a Hybrid Quantum inspired EA, which balances the exploration and exploitation in the search process by adaptively evolving the populations. It employs an adaptive quantum rotation based crossover operator designed by hybridizing a conventional crossover operator with the principles of Quantum Mechanics. The degree of rotation in this operator is determined adaptively. The proposed algorithm does not require either a mutation operator, to avoid premature convergence, or a local heuristic to improve convergence rate. Further, a parameter-tuning free hybrid technique is employed for handling constraints, which overcomes some limitations in the traditional techniques like penalty factor methods, by hybridizing Feasibility Rules method with Adaptive Penalty Factor method. It is implemented by using two populations, each evolving by applying one of the constraints handling techniques and swapping a part of the populations. A standard set of six diverse benchmark engineering design optimization problems have been used for testing the proposed algorithm. The algorithm exhibits superior performance than the existing state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

This paper describes a new algorithm for solving nonlinear programming problems with equality constraints. The method introduces the idea of using trust cylinders to keep the infeasibility under control. Each time the trust cylinder is violated, a restoration step is called and the infeasibility level is reduced. The radius of the trust cylinder has a nonincreasing update scheme, so eventually a feasible (and optimal) point is obtained. Global and local convergence of the algorithm are analyzed, as well as its numerical performance. The results suggest that the algorithm is promising. [ABSTRACT FROM AUTHOR]

This paper presents a quadratically approximate algorithm framework (QAAF) for solving general constrained optimization problems, which solves, at each iteration, a subproblem with quadratic objective function and quadratic equality together with inequality constraints. The global convergence of the algorithm framework is presented under the Mangasarian-Fromovitz constraint qualification (MFCQ), and the conditions for superlinear and quadratic convergence of the algorithm framework are given under the MFCQ, the constant rank constraint qualification (CRCQ) as well as the strong second-order sufficiency conditions (SSOSC). As an incidental result, the definition of an approximate KKT point is brought forward, and the global convergence of a sequence of approximate KKT points is analysed. [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]

This paper proposes a line search technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribière-Polyak conjugate gradient algorithm. It is proved that this line search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the Zoutendijk condition holds under mild assumptions. It is also proved that the resulting conjugate gradient algorithm is convergent under a strong convexity assumption. For the nonconvex case, a globally convergent modification is proposed. Numerical tests are presented. [ABSTRACT FROM AUTHOR]

Global convergence in constrained optimization algorithms has traditionally been enforced by the use of parametrized penalty functions. Recently, the filter strategy has been introduced as an alternative. At least part of the motivation for using filter methods consists of avoiding the need for estimating a suitable penalty parameter, which is often a delicate task. In this paper, we demonstrate that the use of a parametrized penalty function in nonsmooth convex optimization can be avoided without using the relatively complex filter methods. We propose an approach which appears to be more direct and easier to implement, in the sense that it is closer in spirit and structure to the well-developed unconstrained bundle methods. Preliminary computational results are also reported. [ABSTRACT FROM AUTHOR]

Abstract: A directed searching optimization algorithm (DSO) is proposed to solve constrained optimization problems in this paper. The proposed algorithm includes two important operations — position updating and genetic mutation. Position updating enables the non-best solution vectors to mimic the best one, which is beneficial to the convergence of the DSO; genetic mutation can increase the diversity of individuals, which is beneficial to preventing the premature convergence of the DSO. In addition, we adopt the penalty function method to balance objective and constraint violations. We can obtain satisfactory solutions for constrained optimization problems by combining the DSO and the penalty function method. Experimental results indicate that the proposed algorithm can be an efficient alternative on solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: This paper presents an augmented Lagrangian methodology with a stochastic population based algorithm for solving nonlinear constrained global optimization problems. The method approximately solves a sequence of simple bound global optimization subproblems using a fish swarm intelligent algorithm. A stochastic convergence analysis of the fish swarm iterative process is included. Numerical results with a benchmark set of problems are shown, including a comparison with other stochastic-type algorithms. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a kind of QP-free feasible algorithm which solves an inequality constrained nonlinear optimization problem. Under some weaker conditions than those in [H. Qi, L. Qi, A New QP-free, globally convergent, locally superlinear convergent algorithm for inequality constrained optimization, SIAM J. Optim. 11 (2000) 113–132], we prove that the algorithm is implementable and globally convergent. Moreover, some numerical test results are given to indicate that the algorithm is quite promising. [Copyright &y& Elsevier]

We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using iterative linear algebra techniques. We address how to determine when a given inexact step makes sufficient progress toward a solution of the nonlinear program, as measured by an exact penalty function. The method is globalized by a line search. An analysis of the global convergence properties of the algorithm and numerical results are presented. [ABSTRACT FROM AUTHOR]

In this paper, optimization problems with nonlinear inequality constraints are discussed, by combining the sequential quadratic programming (SQP) with an new generalized projection technique, a new feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) is solved and a master direction is obtained, and an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction, both this two correction formulas contain a new generalized projection technique. Under weaker conditions without the strict complementarity, the new algorithm is proved to possess global convergence and superlinear convergence. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. [Copyright &y& Elsevier]

A revised conjugate gradient projection method for nonlinear inequality constrained optimization problems is proposed in the paper, since the search direction is the combination of the conjugate projection gradient and the quasi-Newton direction. It has two merits. The one is that the amount of computation is lower because the gradient matrix only needs to be computed one time at each iteration. The other is that the algorithm is of global convergence and locally superlinear convergence without strict complementary condition under some mild assumptions. In addition the search direction is explicit. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. [Copyright &y& Elsevier]