We study a chance-constrained optimization problem where the random variable appearing in the chance constraint follows a normal distribution whose mean and variance both depend linearly on the decision variables. Suc...
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We study a chance-constrained optimization problem where the random variable appearing in the chance constraint follows a normal distribution whose mean and variance both depend linearly on the decision variables. Such structure may arise in many applications, including the normal approximation to the Poisson distribution. We present a polynomial-time algorithm to solve the resulting nonconvex optimization problem, and illustrate the efficacy of our method using a numerical experiment.
A mathematical programming problem is said to have separated nonconvex variables when the variables can be divided into two groups: x=(x1,...,xn) and y=( y1,..., yn), such that the objective function and any constrain...
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In this paper, we are concerned with a vector reverseconvex minimization problem (P). For such a problem, by means of the so-called Fenchel-Lagrange duality, we provide nec-essary optimality conditions for proper eff...
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In this paper, we are concerned with a vector reverseconvex minimization problem (P). For such a problem, by means of the so-called Fenchel-Lagrange duality, we provide nec-essary optimality conditions for proper efficiency in the sense of Geoffrion. This duality is used after a decomposition of problem (P) into a family of convex vector minimization sub-problems and scalarization of these subproblems. The optimality conditions are expressed in terms of subdifferentials and normal cones in the sense of convex analysis. The obtained results are new in the literature of vector reverse convex programming. Moreover, some of them extend with improvement some similar results given in the literature, from the scalar case to the vectorial one.
We analyze the component testing problem of devices which consist of series connection of redundant, standby redundant and k -out-of- n subsystems. Although system reliability is a common performance measure, here we ...
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We analyze the component testing problem of devices which consist of series connection of redundant, standby redundant and k -out-of- n subsystems. Although system reliability is a common performance measure, here we extend previous studies by considering expected system lifetime. This case applies when setting mission time for a system is more practical than deciding on system reliability accurately. The problem is formulated as a semi-infinite linear programming problem, and the optimum test times are obtained with a column generation technique incorporating reverse convex programming. The proposed solution technique is also illustrated by numerical examples.
In this note we explore duality in reverseconvex optimization with reverseconvex inequality constraints. While we are examining the special case of a finite index set of inequality constraints, we are primarily inte...
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In this note we explore duality in reverseconvex optimization with reverseconvex inequality constraints. While we are examining the special case of a finite index set of inequality constraints, we are primarily interested in the general case of an arbitrary infinite index set with neither extra topological structure nor extra measure structure.
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