This paper presents a practical method for finding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to the non-convex nature of this problem, our approach provides a theoretical guarantee of global optimality. Our algorithm is based on … Read more
The Search Algorithms have been introduced in the paper [3][6] under the name ‘Search via Probability Algorithm’. These optimization techniques converge very fast and are very efficient for solving optimization problems with very large scale feasible domains. But these optimization techniques are not effective in solving the numerical optimization problems with long narrow feasible domains. … Read more
Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact … Read more
group of analytical formulas formulas for calculating the global maximal and minimal ranks and inertias of the quadratic matrix-valued function $$ \phi(X) = \left(\, AXB + C\,\right)\!M\!\left(\, AXB + C \right)^{*} + D $$ are established and their consequences are presented, where $A$, $B$, $C$ and $D$ are given complex matrices with $A$ and $C$ … Read more
Many real-world dynamic problems have constraints, and in certain cases not only the objective function changes over time, but also the constraints. However, there is no research in answering the question of whether current algorithms work well on continuous dynamic constrained optimisation problems (DCOPs), nor is there any benchmark problem that reflects the common characteristics … Read more
We propose a branch-and-bound algorithm for minimizing a not necessarily convex quadratic function over integer variables. The algorithm is based on lower bounds computed as continuous minima of the objective function over appropriate ellipsoids. In the nonconvex case, we use ellipsoids enclosing the feasible region of the problem. In spite of the nonconvexity, these minima … Read more
G. P. McCormick [Math Prog 1976] provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form F(f(z)), where F is a univariate function. Herein, the composition theorem is generalized to allow multivariate outer functions F, and theory for the propagation of subgradients is presented. … Read more
A novel approach for obtaining globally optimal solutions to design of networks with nonlinear resistances and potential driven flows is proposed. The approach is applicable to networks where the potential loss on an edge in the network is governed by a convex and strictly monotonically increasing function of flow rate. We introduce a relaxation of … Read more
In this paper we consider a cardinality-constrained quadratic program that minimizes a convex quadratic function subject to a cardinality constraint and linear constraints. This class of problems has found many applications, including portfolio selection, subset selection and compressed sensing. We propose a successive convex approximation method for this class of problems in which the cardinality … Read more
Analytical formulas are established for calculating the maximal and minimal ranks of the matrix-valued function $A + BXC$ when the rank of $X$ is fixed. Some consequences are also given. ArticleDownload View PDF