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A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
 SIAM Journal on Optimization
, 2001
"... . 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 pr ..."
Abstract

Cited by 56 (0 self)
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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.
An SQP Algorithm For Finely Discretized Continuous Minimax Problems And Other Minimax Problems With Many Objective Functions
, 1996
"... . A common strategy for achieving global convergence in the solution of semiinfinite programming (SIP) problems, and in particular of continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with a progressively finer discretization meshes. Finely discretized min ..."
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Cited by 20 (2 self)
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. A common strategy for achieving global convergence in the solution of semiinfinite programming (SIP) problems, and in particular of continuous minimax problems, is to (approximately) solve a sequence of discretized problems, with a progressively finer discretization meshes. Finely discretized minimax and SIP problems, as well as other problems with many more objectives /constraints than variables, call for algorithms in which successive search directions are computed based on a small but significant subset of the objectives/constraints, with ensuing reduced computing cost per iteration and decreased risk of numerical difficulties. In this paper, an SQPtype algorithm is proposed that incorporates this idea in the particular case of minimax problems. The general case will be considered in a separate paper. The quadratic programming subproblem that yields the search direction involves only a small subset of the objective functions. This subset is updated at each iteration in such a wa...
Oriolo,“A Sensitivity Approach to Optimal Spline Robot
 Trajectories,” Automatica
, 1991
"... planning. AbstrnctA robot trajectory planning problem is considered. Using smooth interpolating cubic splines as joint space trajectories, the path is parameterized in terms of time intervals between knots. A minimum time optimization problem is formulated under maximum torque and velocity constra ..."
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Cited by 17 (0 self)
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planning. AbstrnctA robot trajectory planning problem is considered. Using smooth interpolating cubic splines as joint space trajectories, the path is parameterized in terms of time intervals between knots. A minimum time optimization problem is formulated under maximum torque and velocity constraints, and is solved by means of a first order derivativetype algorithm for semiinfinite nonlinear programming. Feasible directions in the parameter space are generated using sensitivity coefficients of the active constraints. Numerical simulations are reported for a twolink Scara robot. The proposed approach can be used for optimizing more general objective functions under different types of constraints.
Computational Discretization Algorithms For Functional Inequality Constrained Optimization
, 1999
"... In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization ..."
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Cited by 12 (3 self)
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In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization problem. The discretization problem is firstly converted into an optimization problem with a single nonsmooth equality constraint. Since the obtained equality constraint is nonsmooth and does not satisfy the usual constraint qualification condition, relaxation and smoothing techniques are used to approximate the equality constraint via a smooth inequality constraint. This leads to a sequence of approximate smooth optimization problems with one constraint. An adaptive scheme is incorporated into the method to facilitate the computation of the sum in the inequality constraint. The second method is to apply an adaptive scheme directly to the discretization problem. Thus a sequence of optimization problems with a small number of inequality constraints are obtained. Convergence analysis for both methods is established. Numerical examples show that each of the two proposed methods has its own advantages and disadvantages over the other.
Feasible Sequential Quadratic Programming For Finely Discretized Problems From Sip
, 1998
"... A Sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized SemiInfinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few o ..."
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Cited by 8 (1 self)
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A Sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized SemiInfinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the constraints are used in the QP subproblems at each iteration, and (ii) that every iterate satisfies all constraints. 1 INTRODUCTION Consider the SemiInfinite Programming (SIP) problem minimize f(x) subject to \Phi(x) 0; (SI) where f : IR n ! IR is continuously differentiable, and \Phi : IR n ! IR is defined by \Phi(x) \Delta = sup ¸2[0;1] OE(x; ¸); with OE : IR n \Theta [0; 1] ! IR continuously differentiable in the first argument. For an excellent survey of the theory behind the problem (SI), in addition to some algorithms and applications, see [9] as well as the other papers in the present volume. Many globally convergent algorithms designed to solve (SI) 2 Chapter 1...
A new exact penalty function method for continuous inequality constrained optimization problems
 Journal of Industrial and Management Optimization
, 2010
"... publisherauthenticated version online. Alternate Location: Permanent Link: The attached document may provide the author's accepted version of a published work. See Citation for details of the published work. ..."
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publisherauthenticated version online. Alternate Location: Permanent Link: The attached document may provide the author's accepted version of a published work. See Citation for details of the published work.
Dynamic Bundle Methods  Application to Combinatorial Optimization
 MATHEMATICAL PROGRAMMING
, 2005
"... Lagrangian relaxation is a popular technique to solve difficult optimization problems. However, the applicability of this technique depends on having a relatively low number of hard constraints to dualize. When there are exponentially many hard constraints, it is preferable to relax them dynamical ..."
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Cited by 4 (2 self)
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Lagrangian relaxation is a popular technique to solve difficult optimization problems. However, the applicability of this technique depends on having a relatively low number of hard constraints to dualize. When there are exponentially many hard constraints, it is preferable to relax them dynamically, according to some rule depending on which multipliers are active. For instance, only the most violated constraints at a given iteration could be dualized. From the dual point of view, this approach yields multipliers with varying dimensions and a dual objective function that changes along iterations. We discuss how to apply a bundle methodology to solve this kind of dual problems. We analyze the resulting dynamic bundle method giving a positive answer for its convergence properties, including finite termination and a primal result for polyhedral problems. We also report preliminary numerical experience on Linear Ordering and Traveling Salesman Problems.
1FEASIBLE SEQUENTIAL QUADRATIC PROGRAMMING FOR FINELY DISCRETIZED PROBLEMS FROM SIP
"... A Sequential Quadratic Programming algorithm designed to eciently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from nely discretized SemiInnite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the c ..."
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A Sequential Quadratic Programming algorithm designed to eciently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from nely discretized SemiInnite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the constraints are used in the QP subproblems at each iteration, and (ii) that every iterate satises all constraints. 1