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This paper proposes a practical formulation for the non-convex economic dispatch problem to consider multi-fuel options, ramp rate limits, valve loading effect, prohibited operating zones and spinning reserve. A new optimization algorithm based on the θ -bat algorithm ( θ -BA) is suggested to solve the problem. The θ -BA converts the Cartesian search space into the polar coordinates such that more search ability would be achieved. According to the complex, nonlinear, and constrained nature of the problem, a new self-adaptive modification method is proposed. The proposed modified θ -BA ( θ -MBA) is constructed based on the roulette wheel mechanism to effectively increase the convergence of the algorithm. The high ability and satisfying performance of the proposed optimization method is examined on IEEE 15-unit, 40-unit and 100-unit test systems. [ABSTRACT FROM AUTHOR]

By means of Wolfe conditions strategy, we propose a quasi-Newton trust-region method to solve box constrained optimization problems. This method is an adequate combination of the compact limited memory BFGS and the trust-region direction while the generated point satisfies the Wolfe conditions and therefore maintains a positive-definite approximation to the Hessian of the objective function. The global convergence and the quadratic convergence of this method are established under suitable conditions. Finally, we compare our algorithms (IWTRAL and IBWTRAL) with an active set trust-region algorithm (ASTRAL) Xu and Burke (2007) on the CUTEst box constrained test problems presented by Gould et al. (2015). Numerical results show that the presented method is competitive and totally interesting for solving box constrained optimization. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the convergence analysis of a very general class of gradient projection methods for smooth, constrained, possibly nonconvex, optimization. The key features of these methods are the Armijo linesearch along a suitable descent direction and the non Euclidean metric employed to compute the gradient projection. We develop a very general framework from the point of view of block-coordinate descent methods, which are useful when the constraints are separable. In our numerical experiments we consider a large scale image restoration problem to illustrate the impact of the metric choice on the practical performances of the corresponding algorithm. [ABSTRACT FROM AUTHOR]

We propose a novel actor–critic algorithm with guaranteed convergence to an optimal policy for a discounted reward Markov decision process. The actor incorporates a descent direction that is motivated by the solution of a certain non-linear optimization problem. We also discuss an extension to incorporate function approximation and demonstrate the practicality of our algorithms on a network routing application. [ABSTRACT FROM AUTHOR]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Abstract: The alternating direction method of multipliers (ADMM) is known to be a classic and efficient method for constrained optimization problem with two blocks of variables, and its empirical efficiency has been well illustrated in various fields. Specially, for improving its speed performance, Ye and Yuan suggested to do an additional extension with an optimal step size on the variables after each iteration of the primary ADMM. Indeed, the numerical experiments indicate that this modified ADMM improves the speed performance of the ADMM by around 40% without changing the algorithmic framework much. Recently, the convergence rate of the primary ADMM is established. Inspired by its idea, in this paper, we show that this improved ADMM also has convergence rate. The reason that larger γ yields better speed performance is also investigated and explained. [Copyright &y& Elsevier]

Abstract: We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a Byrd–Omojokun-type trust region strategy. Measures of optimality and infeasibility are computed, whose relationship serves as a criterion on which the algorithm decides which one to focus on improving. As a result, the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence. By using a second order correction strategy, Marato’s effect is avoided and fast local convergence is shown. The preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: In this paper, a trust-region sequential quadratic programming algorithm with a modified filter acceptance mechanism is proposed for nonlinear equality constrained optimization. The most important advantage of the proposed algorithm is its avoidance of any feasibility restoration phase, a necessity in traditional filter methods. We solve quadratic programming subproblems based on the well-known Byrd–Omojokun trust-region method. Inexact solutions to these subproblems are allowed. Under some standard assumptions, global convergence of the proposed algorithm is established. Numerical results show our approach is potentially useful. [Copyright &y& Elsevier]

Abstract: In this paper, we consider numerical simulation to a class of constrained dynamic problems where the overall dynamics are determined by the interactions between two sub-systems. We present an iterative algorithm that naturally decouples the computation of the two sub-systems and that ensures an accurate and efficient solution procedure. We conduct rigorous error analysis for the convergence of the iterative algorithm, and verify the analytical results through careful numerical tests. [Copyright &y& Elsevier]

Abstract: A new trust-region algorithm for solving a constrained optimization problem is introduced. In this algorithm, an active set strategy is used together with multiplier method to convert the computation of the trial step to easy trust-region subproblem similar to this for the unconstrained case. A convergence theory for this algorithm is presented. Under reasonable assumptions, it is shown that the algorithm is globally convergent. In particular, it is shown that, in the limit, a subsequence of the iteration sequence satisfies one of four types of stationary conditions. Namely, the infeasible Mayer–Bliss conditions, Fritz John’s conditions, the infeasible Fritz John’s conditions or KKT conditions. Preliminary numerical experiment on the algorithm is presented. The performance of the algorithm is reported. The numerical results show that our approach is of value and merit further investigation. [Copyright &y& Elsevier]

Abstract: Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections (derived from the idea of conjugate directions) of the used difference vectors, utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. Global convergence of the algorithm is established for convex sufficiently smooth functions. Numerical experiments indicate that the new method often improves the L-BFGS method significantly. [Copyright &y& Elsevier]

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, a new line search filter algorithm for equality constrained optimization is presented. The approach belongs to the class of inexact Newton-like methods. It can also be regarded as an inexact version of generic sequential quadratic programming (SQP) methods. The trial step is obtained by truncatedly solving the primal–dual system based on any robust and efficient linear system solver. Practical termination tests for the linear system solver are established to ensure global convergence. Preliminary numerical results demonstrate the approach is potentially useful. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the development of general-purpose algebraic flux correction schemes for continuous (linear and multilinear) finite elements. In order to enforce the discrete maximum principle (DMP), we modify the standard Galerkin discretization of a scalar transport equation by adding diffusive and antidiffusive fluxes. The result is a nonlinear algebraic system satisfying the DMP constraint. An estimate based on variational gradient recovery leads to a linearity-preserving limiter for the difference between the function values at two neighboring nodes. A fully multidimensional version of this scheme is obtained by taking the sum of local bounds and constraining the total flux. This new approach to algebraic flux correction provides a unified treatment of stationary and time-dependent problems. Moreover, the same algorithm is used to limit convective fluxes, anisotropic diffusion operators, and the antidiffusive part of the consistent mass matrix. The nonlinear algebraic system associated with the constrained Galerkin scheme is solved using fixed-point defect correction or a nonlinear SSOR method. A dramatic improvement of nonlinear convergence rates is achieved with the technique known as Anderson acceleration (or Anderson mixing). It blends a number of last iterates in a GMRES fashion, which results in a Broyden-like quasi-Newton update. The numerical behavior of the proposed algorithms is illustrated by a grid convergence study for convection-dominated transport problems and anisotropic diffusion equations in 2D. [Copyright &y& Elsevier]

Abstract: We consider an efficient trust-region framework which employs a new nonmonotone line search technique for unconstrained optimization problems. Unlike the traditional nonmonotone trust-region method, our proposed algorithm avoids resolving the subproblem whenever a trial step is rejected. Instead, it performs a nonmonotone Armijo-type line search in direction of the rejected trial step to construct a new point. Theoretical analysis indicates that the new approach preserves the global convergence to the first-order critical points under classical assumptions. Moreover, superlinear and quadratic convergence are established under suitable conditions. Numerical experiments show the efficiency and effectiveness of the proposed approach for solving unconstrained optimization problems. [Copyright &y& Elsevier]

Abstract: Elimination methods are highly effective for the solution of linear and nonlinear systems of equations, but reversal of the elimination principle can be beneficial as well: competent incorporation of additional independent constraints and variables or more generally immersion of the original computational problem into a larger task, defined by a larger number of independent constraints and variables can improve global convergence of iterative algorithms, that is their convergence from the start. A well known example is the dual linear and nonlinear programming, which enhances the power of optimization algorithms. We believe that this is just an ad hoc application of general Principle of Expansion with Independent Constraints; it should be explored systematically for devising iterative algorithms for the solution of equations and systems of equations and for optimization. At the end of this paper we comment on other applications and extensions of this principle. Presently we show it at work for the approximation of a single zero of a univariate polynomial of a degree . Empirical global convergence of the known algorithms for this task is much weaker than that of the algorithms for all zeros, such as Weierstrass–Durand–Kerner’s root-finder, which reduces its root-finding task to Viète’s (Vieta’s) system of polynomial equations with unknowns. We adjust this root-finder to the approximation of a single zero of , preserve its fast global convergence and decrease the number of arithmetic operations per iteration from quadratic to linear. Together with computing a zero of a polynomial , the algorithm deflates this polynomial as by-product, and then could be reapplied to the quotient to approximate the next zero of . Alternatively by using processors that exchange no data, one can concurrently approximate up to zeros of . Our tests confirm the efficiency of the proposed algorithms. Technically our root-finding boils down to computations with structured matrices, polynomials and partial fraction decompositions. Our study of these links can be of independent interest; e.g., as by-product we express the inverse of a Sylvester matrix via its last column, thus extending the celebrated result of Gohberg and Sementsul (1972) from Toeplitz to Sylvester matrix inverses. [Copyright &y& Elsevier]

Abstract: Combining the norm-relaxed sequential quadratic programming (SQP) method and the idea of method of quasi-strongly sub-feasible directions (MQSSFD) with active set identification technique, a new SQP algorithm for solving nonlinear inequality constrained optimization is proposed. Unlike the previous work, at each iteration of the proposed algorithm, the norm-relaxed quadratic programming (QP) subproblem only consists of the constraints corresponding to an active identification set. Moreover, the high-order correction direction (used to avoid the Maratos effect) is yielded by solving a system of linear equations (SLE) which also includes only the constraints and their gradients corresponding to the active identification set, therefore, the scale and the computation cost of the high-order correction directions are further decreased. The arc search in our algorithm can effectively combine the initialization processes with the optimization processes, and the iteration points can get into the feasible set after a finite number of iterations. Furthermore, the arc search conditions are weaker than the previous work, and the computation cost is further reduced. The global convergence is proved under the Mangasarian–Fromovitz constraint qualification (MFCQ). If the strong second-order sufficient conditions are satisfied, then the active constraints are exactly identified by the identification set. Without the strict complementarity, superlinear convergence can be obtained. Finally, some elementary numerical results are reported. [Copyright &y& Elsevier]

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: 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 use a projected gradient algorithm to solve a nonlinear operator equation with -norm constraint. Gradient iterations with -norm constraints have been studied recently both in the context of inverse problem and of compressed sensing. In this paper, the constrained gradient iteration is implemented via a projected operator. We establish the -norm convergence of sequence constructed by the constrained gradient iteration when . The performance of the method is testified by a numerical example. [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 proposes a line search filter reduced Hessian method for nonlinear equality constrained optimization. The feature of the presented algorithm is that the reduced Hessian method is used to produce a search direction, a backtracking line search procedure to generate step size, some filtered rules to determine step acceptance, second order correction technique to reduce infeasibility and overcome the Maratos effects. It is shown that this algorithm does not suffer from the Maratos effects by using second order correction step, and under mild assumptions fast convergence to second order sufficient local solutions is achieved. The numerical experiment is reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In many mountainous areas, landslides and slope instabilities frequently occur after heavy rainfall and earthquake, and result in enormous casualties and huge economic losses. In order to mitigate the landslides hazard efficiently, a method is required for a better understanding of stability analysis. Fortunately, upper bound theorem of limit analysis provides a practical and effective upper bound approach to evaluate the stability of slopes. And in this approach, the search for the minimum factor of safety can be formulated as a nonlinear constrained optimization. In general, the SQP-type algorithms are used to solve this optimization problem. However, it is quite time consuming and difficult to search the optimum from an arbitrary starting point based on the SQP-type algorithms. Fortunately, a QP-free algorithm based on penalty function and active-set strategy can be globally convergent toward the KKT points with arbitrary starting point, and the rate of convergence is local superlinear or even quadratic. Two classical problems of slope stability are solved by this QP-free algorithm. The results show that the QP-free algorithm would be the better choice than SQP-type algorithms for solving the nonlinear constrained optimization problem which is derived from the upper bound limit analysis of slope stability. [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 new continuous formulation for the zero-one programming problem is presented, followed by an investigation of the algorithm for it. This paper first reformulates the zero-one programming problem as an equivalent mathematical programs with complementarity constraints, then as a smooth ordinary nonlinear programming problem with the help of the Fischer–Burmeister function. After that the augmented Lagrangian method is introduced to solve the resulting continuous problem, with optimality conditions for the non-smooth augmented Lagrangian problem derived on the basis of approximate smooth variational principle, and with convergence properties established. To our benefit, the sequence of solutions generated converges to feasible solutions of the original problem, which provides a necessary basis for the convergence results. [ABSTRACT FROM AUTHOR]

Abstract: The learning speed of an adaptive algorithm can be improved by properly constraining the cost function of the adaptive algorithm. In this work, a noise-constrained least mean fourth (NCLMF) adaptive algorithm is proposed. The NCLMF algorithm is obtained by constraining the cost function of the standard LMF algorithm to the fourth-order moment of the additive noise. The NCLMF algorithm can be seen as a variable step-size LMF algorithm. The main aim of this work is to derive the NCLMF adaptive algorithm, analyze its convergence behavior, and assess its performance in different noise environments. Furthermore, the analysis of the proposed NCLMF algorithm is carried out using the concept of energy conservation. Finally, a number of simulation results are carried out to corroborate the theoretical findings, and as expected, improved performance is obtained through the use of this technique over the traditional LMF algorithm. [Copyright &y& Elsevier]

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: The aim of this paper is to incorporate the preconditioned gradient path in a nonmonotone stabilization algorithm for unconstrained optimization. The global convergence and locally superlinear convergence are established for this class of algorithms. Finally, we report in details the numerical results which show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: A numerical algorithm is presented to solve the constrained weighted energy problem from potential theory. As one of the possible applications of this algorithm, we study the convergence properties of the rational Lanczos iteration method for the symmetric eigenvalue problem. The constrained weighted energy problem characterizes the region containing those eigenvalues that are well approximated by the Ritz values. The region depends on the distribution of the eigenvalues, on the distribution of the poles, and on the ratio between the size of the matrix and the number of iterations. Our algorithm gives the possibility of finding the boundary of this region in an effective way. We give numerical examples for different distributions of poles and eigenvalues and compare the results of our algorithm with the convergence behavior of the explicitly performed rational Lanczos algorithm. [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: A derivative-free simulated annealing driven multi-start algorithm for continuous global optimization is presented. We first propose a trial point generation scheme in continuous simulated annealing which eliminates the need for the gradient-based trial point generation. We then suitably embed the multi-start procedure within the simulated annealing algorithm. We modify the derivative-free pattern search method and use it as the local search in the multi-start procedure. We study the convergence properties of the algorithm and test its performance on a set of 50 problems. Numerical results are presented which show the robustness of the algorithm. Numerical comparisons with a gradient-based simulated annealing algorithm and three population-based global optimization algorithms show that the new algorithm could offer a reasonable alternative to many currently available global optimization algorithms, specially for problems requiring ‘direct search’ type algorithm. [Copyright &y& Elsevier]

Abstract: We propose a novel hybrid algorithm named PSO-DE, which integrates particle swarm optimization (PSO) with differential evolution (DE) to solve constrained numerical and engineering optimization problems. Traditional PSO is easy to fall into stagnation when no particle discovers a position that is better than its previous best position for several generations. DE is incorporated into update the previous best positions of particles to force PSO jump out of stagnation, because of its strong searching ability. The hybrid algorithm speeds up the convergence and improves the algorithm’s performance. We test the presented method on 11 well-known benchmark test functions and five engineering optimization functions. Comparisons show that PSO-DE outperforms or performs similarly to seven state-of-the-art approaches in terms of the quality of the resulting solutions. [Copyright &y& Elsevier]

Abstract: We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix , subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples. [Copyright &y& Elsevier]

Abstract: In this paper, a new descent algorithm for solving unconstrained optimization problem is presented. Its search direction is descent and line search procedure can be avoided except for the first iteration. It is globally convergent under mild conditions. The search direction of the new algorithm is generalized and convergence of corresponding algorithm is also proved. Numerical results show that the algorithm is efficient for given test problems. [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: We analyze an active set quasi-Newton method for large scale bound constrained problems. Our approach combines the accurate active set identification function and the projected search. Both of these strategies permit fast change in the working set. The limited memory method is employed to update the inactive variables, while the active variables are updated by simple rules. A further division of the active set enables the global convergence of the new algorithm. Numerical tests demonstrate the efficiency and performance of the present strategy and its comparison with some existing active set strategies. [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]

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]

A new optimization technique, multiobjective optimization immune algorithm for constrained nonlinear multiobjective optimization problems is designed based on immune metaphors of humoral immune and Pareto optimality, especially, some interactive metaphors between antigen population and antibody population. It includes four main mechanisms: [(1)] constraint-handling operation that provides an alternative feasible solution set for rapidly finding Pareto optimal solutions; [(2)] antibody evolution associated with clonal selection principle and ideas of immune regulation; competition and update of antigens that induces evolution of antibody populations; [(3)] memory pool used for collecting the best solutions of evolving antibody populations. Convergence is proven through Markov theory as well as demonstrated by the experiment results. Comparative analysis and applications illustrate that it is effective and valuable. [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]

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]

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]