Crane scheduling in container terminals is known as a difficult optimization problem that has become even more challenging in recent years with the proliferation of multi-gantry automated stacking cranes. In this paper we present an efficient algorithm solving a subproblem arising in this context, namely deciding the priority of cranes after transportation tasks have been … Read more
This paper studies the $H^1$ Sobolev seminorm of quadratic functions. The research is motivated by the least-norm interpolation that is widely used in derivative-free optimization. We express the $H^1$ seminorm of a quadratic function explicitly in terms of the Hessian and the gradient when the underlying domain is a ball. The seminorm gives new insights … Read more
A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. GRASP heuristics are multistart procedures which apply local search to a set of starting solutions generated with a randomized greedy algorithm or semi-greedy method. The best local optimum found over the iterations is returned as the heuristic solution. Path-relinking is a search … Read more
We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only … Read more
We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained quadratic programs (MIQCQP) to epsilon-global optimality. The facets of low-dimensional (n < 4) edge-concave aggregations dominating the termwise relaxation of MIQCQP are introduced at every node of a branch-and-bound tree. Concave multivariable ... Read more
A hybrid HS and PRP type conjugate gradient method for smooth optimization is presented, which reduces to the classical RPR or HS method if exact linear search is used and converges globally and R-linearly for nonconvex functions with an inexact backtracking line search under standard assumption. An inexact version of the proposed method which admits … Read more
We introduce a framework for robustifying portfolio selection problems with respect to ambiguity in the distribution of the random asset losses. In particular, we are interested in convex, version independent risk measures. To robustify these risk measures, we use an ambiguity set which is defined as a neighborhood around a reference probability measure which represents … Read more
This paper is devoted to study the Lipschitzian/Holderian type global error bound for systems of many finitely convex polynomial inequalities over a polyhedral constraint. Firstly, for systems of this type, we show that under a suitable asymtotic qualification condition, the Lipschitzian type global error bound property is equivalent to the Abadie qualification condition, in particular, … Read more
In this paper we study the t-branch split cuts introduced by Li and Richard (2008). They presented a family of mixed-integer programs with n integer variables and a single continuous variable and conjectured that the convex hull of integer solutions for any n has unbounded rank with respect to (n-1)-branch split cuts. It was shown … Read more
All manifestations of dimensional harmony in nature and human practice are being always characterized by deviations from golden ratio that often makes their acceptance problematic. On the example of Fechner’s experiments the paper discusses the way of solving this problem, based on informational approach, according to which the informatively optimal permissible deviation from dimensional harmony … Read more