We are concerned with concave programming or the convex maximization problem. In this paper, we propose a method and algorithm for solving the problem which are based on the global optimality conditions first obtained...
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We are concerned with concave programming or the convex maximization problem. In this paper, we propose a method and algorithm for solving the problem which are based on the global optimality conditions first obtained by Strekalovsky (Soviet Mathematical Doklady, 8(1987)). The method continues approaches given in (Journal of global optimization, 8(1996);Journal of Nolinear and convex Analyses 4(1)(2003)). Under certain assumptions a convergence property of the proposed method has been established. Some computational results are reported. Also, it has been shown that the problem of finding the largest eigenvalue can be found by the proposed method.
This paper presents a motion control algorithm for a planar mobile observer such as, e.g., a mobile robot equipped with an omni-directional camera. We propose a nonsmooth gradient algorithm for the problem of maximizi...
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ISBN:
(纸本)0780390989
This paper presents a motion control algorithm for a planar mobile observer such as, e.g., a mobile robot equipped with an omni-directional camera. We propose a nonsmooth gradient algorithm for the problem of maximizing the area of the region visible to the observer in a simple nonconvex polygon. First, we show that the visible area is almost everywhere a locally Lipschitz function of the observer location. Second, we provide a novel version of LaSalle Invariance Principle for discontinuous vector fields and Lyapunov functions with a finite number of discontinuities. Finally, we establish the asymptotic convergence properties of the nonsmooth gradient algorithm and we illustrate numerically its performance.
This paper is concerned with the robust control problem of linear fractional representation (LFT) uncertain systems depending on a time-varying parameter uncertainty. Our main result exploits a linear matrix inequalit...
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This paper is concerned with the robust control problem of linear fractional representation (LFT) uncertain systems depending on a time-varying parameter uncertainty. Our main result exploits a linear matrix inequality (LMI) characterization involving scalings and Lyapunov variables subject to an additional essentially nonconvex algebraic constraint. The nonconvexity enters the problem in the form of a rank deficiency condition or matrix inverse relation on the scalings only. It is shown that such problems, but also more generally rank inequalities and bilinear constraints, can be formulated as the minimization of a concave functional subject to LMI constraints. First of all, a local Frank and Wolfe (FW) feasible direction algorithm is introduced in this context to tackle this hard optimization problem. Exploiting the attractive concavity structure of the problem, several efficient global concave programming methods are then introduced and combined with the local feasible direction method to secure and certify global optimality of the solutions. Computational experiments indicate the viability of our algorithms, and in the worst case, they require the solution of a few LMI programs.
The production functions are considered as functions of values of concave programming problems. Some properties of the functions, in particular, the property of homogeneity and linear homogeneity, are investigated. Ex...
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The production functions are considered as functions of values of concave programming problems. Some properties of the functions, in particular, the property of homogeneity and linear homogeneity, are investigated. Examples of the construction of such functions are presented.
first examined the problem of separable concave programming more than thirty years ago, making it one of the earliest branches of nonlinear programming to be explored. This paper proposes a new algorithm that finds th...
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first examined the problem of separable concave programming more than thirty years ago, making it one of the earliest branches of nonlinear programming to be explored. This paper proposes a new algorithm that finds the exact global minimum of this problem in a finite number of iterations. In addition to proving that our algorithm terminates finitely, the paper extends a guarantee of finiteness to all branch and-bound algorithms for concave programming that (1) partition exhaustively using rectangular subdivisions and (2) branch on the incumbent solution when possible. The algorithm uses domain reduction techniques to accelerate convergence;it solves problems with as many as 100 nonlinear variables, 400 linear variables and 50 constraints in about five minutes on an IBM RS/6000 Power PC. An industrial application with 152 nonlinear variables, 593 linear variables, and 417 constraints is also solved in about ten minutes.
The purpose of this paper is to give new formulations for the unconstrained 0-1 nonlinear problem. The unconstrained 0-1 nonlinear problem is reduced to nonlinear continuous problems where the objective functions are ...
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Local convergence results of the convex minorant (CM) algorithm to obtain the nonparametric maximum-likelihood estimator of a distribution under interval-censored observations are given. We also provide a variation of...
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We propose a new algorithm to solve the on-line vertex enumeration problem for polytopes, doing all computations in n-space, where n is the dimension of the polytope. This algorithm exploits adjacency lists between ve...
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We propose a new algorithm to solve the on-line vertex enumeration problem for polytopes, doing all computations in n-space, where n is the dimension of the polytope. This algorithm exploits adjacency lists between vertices and uses no simplex tableaux. It can handle the cases of empty or degenerate polyhedra. A theoretical and numerical comparison with existing approaches for off-line vertex enumeration is presented.
A method is described for globally minimizing concave functions over convex sets whose defining constraints may be nonlinear. The algorithm generates linear programs whose solutions minimize the convex envelope of the...
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A method is described for globally minimizing concave functions over convex sets whose defining constraints may be nonlinear. The algorithm generates linear programs whose solutions minimize the convex envelope of the original function over successively tighter polytopes enclosing the feasible region. The algorithm does not involve cuts of the feasible region, requires only simplex pivot operations and univariate search computations to be performed, allows the objective function to be lower semicontinuous and nonseparable, and is guaranteed to converge to the global solution. Computational aspects of the algorithm are discussed.
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