This article presents a primal-dual predictor-corrector interior-point method for solving quadratically constrained convex optimization problems that arise from truss design problems. We investigate certain special fe...
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This article presents a primal-dual predictor-corrector interior-point method for solving quadratically constrained convex optimization problems that arise from truss design problems. We investigate certain special features of the problem, discuss fundamental differences of interior-point methods for linearly and nonlinearly constrained problems, extend Mehrotra's predictor-corrector strategy to nonlinear programs, and establish convergence of a long step method. Numerical experiments on large scale problems illustrate the surprising efficiency of the method.
Using extended quadratic Lyapunov functions, we consider H ∞ control synthesis problems for input-affine polynomial type nonlinear systems, and characterize nonlinear H ∞ controllers, in the state feedback case and ...
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Using extended quadratic Lyapunov functions, we consider H ∞ control synthesis problems for input-affine polynomial type nonlinear systems, and characterize nonlinear H ∞ controllers, in the state feedback case and the output feedback case, via Riccati type matrix inequality conditions. The controllers can be given by solving linear matrix inequalities which are given at vertices of a convex hull enclosing a domain of states. We also detennine a domain of internal stability. We finally show that the proposed method is effective through a numerical example for output feedback control problem of bilinear system.
In this paper an iterative algorithm for solving the problem of optimal time moving of a linear system from the initial state to the given convex compact. has been proposed. Global convergence of the algorithm is proved.
In this paper an iterative algorithm for solving the problem of optimal time moving of a linear system from the initial state to the given convex compact. has been proposed. Global convergence of the algorithm is proved.
Question on existence of conditional approximation minimum points are considered. Is shown, that the set of points conditional approximation minimum even in case of convex functions can not cut with set approximation ...
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Question on existence of conditional approximation minimum points are considered. Is shown, that the set of points conditional approximation minimum even in case of convex functions can not cut with set approximation saddle points. However in a limit on parameter r ( r ↓ 0) these sets converge to set of points of a conditional minimum.
A modification of the programming iterations method is described here for the discrete-time controlled dynamical systems in which spaces of controls and phase states are the spaces with a priori given notion of limit ...
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A modification of the programming iterations method is described here for the discrete-time controlled dynamical systems in which spaces of controls and phase states are the spaces with a priori given notion of limit of a sequence, i. e. the L * -spaces. For such systems described by nonlinear relations it is to be considered the game problem of keeping back of the system within given phase restrictions during an infinite time interval. The modification of the programming iterations method is used for solving the game problem for the first player on the classes of counterstrategies and quasistrategies.
In this paper hierarchical multicriteria optimization problems are addressed in a convex programming framework. It is assumed that the criteria are aggregated into a nonlinear function, which renders the problem nonse...
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作者：
STURM, JFZHANG, SStudent
Assistant Professor Department of Econometrics University of Groningen Groningen The Netherlands
In this paper, we introduce a potential reduction method for harmonically convex programming. We show that, if the objective function and the m constraint functions are all k-harmonically convex in the feasible set, t...
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In this paper, we introduce a potential reduction method for harmonically convex programming. We show that, if the objective function and the m constraint functions are all k-harmonically convex in the feasible set, then the number of iterations needed to find an is-an-element-of-optimal solution is bounded by a polynomial in m, k, and log(1/is-an-element-of). The method requires either the optimal objective value of the problem or an upper bound of the harmonic constant k as a working parameter. Moreover, we discuss the relation between the harmonic convexity condition used in this paper and some other convexity and smoothness conditions used in the literature.
We present a log-barrier based algorithm for linearly constrained convex differentiable programming problems in nonnegative variables, but where the objective function may not be differentiable at points having a zero...
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We present a log-barrier based algorithm for linearly constrained convex differentiable programming problems in nonnegative variables, but where the objective function may not be differentiable at points having a zero coordinate. We use an approximate centering condition as a basis for decreasing the positive parameter of the log-barrier term and show that the total number of iterations to achieve an is-an-element-of-tolerance optimal solution is O(\log(is-an-element-of)\) x (number of inner-loop iterations). When applied to the n-variable dual geometric programming problem, this bound becomes O(n2U/is-an-element-of), where U is an upper bound on the maximum magnitude of the iterates generated during the computation.
We present a primal-dual row-action method for the minimization of a convex function subject to general convex constraints. Constraints are used one at a time, no changes are made in the constraint functions and their...
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We present a primal-dual row-action method for the minimization of a convex function subject to general convex constraints. Constraints are used one at a time, no changes are made in the constraint functions and their Jacobian matrix (thus, the row-action nature of the algorithm), and at each iteration a subproblem is solved consisting of minimization of the objective function subject to one or two linear equations. The algorithm generates two sequences: one of them, called primal, converges to the solution of the problem;the other one, called dual, approximates a vector of optimal KKT multipliers for the problem. We prove convergence of the primal sequence for general convex constraints. In the case of linear constraints, we prove that the primal sequence converges at least linearly and obtain as a consequence the convergence of the dual sequence.
The paper presents a logarithmic barrier cutting plane algorithm for convex (possibly non-smooth, semi-infinite) programming. Most cutting plane methods, like that of Kelley, and Cheney and Goldstein, solve a linear a...
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The paper presents a logarithmic barrier cutting plane algorithm for convex (possibly non-smooth, semi-infinite) programming. Most cutting plane methods, like that of Kelley, and Cheney and Goldstein, solve a linear approximation (localization) of the problem and then generate an additional cut to remove the linear program's optimal point. Other methods, like the ''central cutting'' plane methods of Elzinga-Moore and Goffin-Vial, calculate a center of the linear approximation and then adjust the level of the objective, or separate the current center from the feasible set. In contrast to these existing techniques, we develop a method which does not solve the linear relaxations to optimality, but rather stays in the interior of the feasible set. The iterates follow the central path of a linear relaxation, until the current iterate either leaves the feasible set or is too close to the boundary. When this occurs, a new cut is generated and the algorithm iterates. We use the tools developed by den Hertog, Roos and Terlaky to analyze the effect of adding and deleting constraints in long-step logarithmic barrier methods for linear programming. Finally, implementation issues and computational results are presented. The test problems come from the class of numerically difficult convex geometric and semi-infinite programming problems.
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