Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse.

this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can

CFSQP is a set of C functions for the minimization of the maximum of a set of smooth objective functions (possibly a single one, or even none at all) subject to general smooth constraints (if there is no objective function, the goal is to simply find a point satisfying the constraints). If the initial guess provided by the user is infeasible for some inequality constraint or some linear equality constraint, CFSQP first generates a feasible point for these constraints; subsequently the successive iterates generated by CFSQP all satisfy these constraints. Nonlinear equality constraints are turned into inequality constraints (to be satisfied by all iterates) and the maximum of the objective functions is replaced by an exact penalty function which penalizes nonlinear equality constraint violations only. When solving problems with many sequentially related constraints (or objectives), such as discretized semiinfinite programming (SIP) problems, CFSQP gives the user the option to use an algo...

Using a simple analytical example, we demonstrate that a class of interior point methods for general nonlinear programming, including some current methods, is not globally convergent. It is shown that those algorithms do produce limit points that are neither feasible nor stationary points of some measure of the constraint violation, when applied to a well-posed problem. 1 Introduction Over the past decade a variety of interior point methods for nonconvex nonlinear programming (NLP) have been proposed and found to be efficient in practice (see e.g. [1]--[4], [6]--[8], [10]--[12]). Based on earlier work [5], these methods come in different varieties, such as primal or primal-dual methods, line search or trust region methods, with different merit functions, different strategies to update the barrier parameter, etc. For some algorithms, theoretical global convergence properties have been proved. It has been shown that under certain assumptions the considered method converges to a loca...

We present two extensions to the Space Carving framework. The first is a progressive scheme to better reconstruct surfaces lacking sufficient textures. The second is a novel photo-consistency measure that is valid for both specular and diffuse surfaces, under unknown lighting conditions. 1

. Extension of quasi-Newton techniques from unconstrained to constrained optimization via Sequential Quadratic Programming (SQP) presents several difficulties. Among these are the possible inconsistency, away from the solution, of first order approximations to the constraints, resulting in infeasibility of the quadratic programs; and the task of selecting a suitable merit function, to induce global convergence. In the case of inequality constrained optimization, both of these difficulties disappear if the algorithm is forced to generate iterates that all satisfy the constraints, and that yield monotonically decreasing objective function values. (Feasibility of the successive iterates is in fact required in many contexts such as in real-time applications or when the objective function is not well defined outside the feasible set). It has been recently shown that this can be achieved while preserving local two-step superlinear convergence. In this note, the essential ingredients for an S...

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. A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast local convergence properties. A preliminary implementation has been tested and some promising numerical results are reported. Key words. sequential quadratic programming, SQP, feasible iterates, feasible SQP, FSQP AMS subject classifications. 49M37, 65K05, 65K10, 90C30, 90C53 PII. S1052623498344562 1.

This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver. A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of about 3 improvement over branch-and-bound is observed...

FFSQP is a set of FORTRAN subroutines for the minimization of the maximum of a set of smooth objective functions (possibly a single one, or even none at all) subject to general smooth constraints (if there is no objective function, the goal is to simply find a point satisfying the constraints). If the initial guess provided by the user is infeasible for some inequality constraint or some linear equality constraint, FFSQP first generates a feasible point for these constraints; subsequently the successive iterates generated by FFSQP all satisfy these constraints. Nonlinear equality constraints are turned into inequality constraints (to be satisfied by all iterates) and the maximum of the objective functions is replaced by an exact penalty function which penalizes nonlinear equality constraint violations only. The user has the option of either requiring that the (modified) objective function decrease at each iteration after feasibility for nonlinear inequality and linear constraints has b...