Recently, we proposed an algorithm for binary tomography based on dc (difference of convex functions) programming [T. Pham dinh, L.T. Hoai An, A d.c. optimization algorithm for solving the trust-region subproblem, SIA...
详细信息
A so-calleddcA method based on a d.c. (difference of convex functions) optimization approach (algorithm) for solving large-scale distance geometry problems is developed. different formulations of equivalent d.c. prog...
详细信息
A so-calleddcA method based on a d.c. (difference of convex functions) optimization approach (algorithm) for solving large-scale distance geometry problems is developed. different formulations of equivalent d.c. programs in the l(1)-approach are stated via the Lagrangian duality without gap relative to d.c. programming, and new nonstandard nonsmooth reformulations in the l(infinity)-approach (resp., the l(1)-l(infinity)-approach) are introd.c.d. Substantial subdifferential calculations permit us to compute sequences of iterations in the dcA quite simply. The computations actually require matrix-vector prod.c.s and only one cholesky factorization (resp., with an additional solution of a convex program) in the l(1)-approach (resp., the l(1)-l(infinity)-approach) and allow the exploitation of sparsity in the large-scale setting. Two techniques-respectively, using shortest paths between all pairs of atoms to generate the complete dissimilarity matrix and the spanning trees procedure are investigated in order to compute a good starting point for the dcA. Finally, many numerical simulations of the molecular optimization problems with up to 12567 variables are reported, which prove the practical usefulness of the nonstandard nonsmooth reformulations, the globality of found solutions, and the robustness and efficiency of our algorithms.
This paper addresses itself to a portfolio optimization problem under nonconvex transaction costs and minimal transaction unit constraints. Associated with portfolio construction is a fee for purchasing assets. Unit t...
详细信息
This paper addresses itself to a portfolio optimization problem under nonconvex transaction costs and minimal transaction unit constraints. Associated with portfolio construction is a fee for purchasing assets. Unit transaction fee is larger when the amount of transaction is smaller. Hence the transaction cost is usually a concave function up to certain point. When the amount of transaction increases, the unit price of assets increases due to illiquidity/market impact effects. Hence the transaction cost becomes convex beyond.c.rtain bound. Therefore, the net expected return becomes a general d.c. function (difference of two convex functions). We will propose a branch-and-bound algorithm for the resulting d.c. maximization problem subject to a constraint on the level of risk measured in terms of the absolute deviation of the rate of return of a portfolio. Also, we will show that the minimal transaction unit constraints can be incorporated without excessively increasing the amount of computation.
In this paper, we propose an algorithm for globally solving optimization problems over efficient sets. The algorithm is established based on a branch and bound scheme in which the bounding procedure is performed by us...
详细信息
In this paper, we propose an algorithm for globally solving optimization problems over efficient sets. The algorithm is established based on a branch and bound scheme in which the bounding procedure is performed by using the well known weak duality theorem in Lagrange duality. A suitable combination of this algorithm with a local search procedure in d.c. optimization (nameddcA) leads to a promising global algorithm, whose efficiency is more or less confirmed by computational experiments on a large set of test problems. (c) 2002 Elsevier Science B.V. All rights reserved.
This paper presents numerical computations for solving the BMI problem. Four global algorithms including two parallel algorithms are employed to solve the BMI problem by a sequence of concave minimization problems or ...
详细信息
This paper presents numerical computations for solving the BMI problem. Four global algorithms including two parallel algorithms are employed to solve the BMI problem by a sequence of concave minimization problems or d.c. programs via concave programming. The parallel algorithms with or based on a suitable partition of an initial enclosing ployhedron are more efficient than the serial ones. computational experiences are reported for randomly generated BMI problems of small size.
We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed.c.nvex set in ℝn. This algorithm combines a new prismatic branch and bo...
详细信息
The following problem is studied: Given a compact setS inR n and a Minkowski functionalp(x), find the largest positive numberr for which there existsx ∈ S such that the set of ally ∈ R n satisfyingp(y?x) ≤ r is...
详细信息
The following problem is studied: Given a compact setS inR class="a-plus-plus"> n and a Minkowski functionalp(x), find the largest positive numberr for which there existsx ∈ S such that the set of ally ∈ R class="a-plus-plus"> n satisfyingp(y?x) ≤ r is contained inS. It is shown that whenS is the intersection of a closed.c.nvex set and several complementary convex sets (sets whose complements are open convex) this “design centering problem” can be reformulated as the minimization of some d.c. function (difference of two convex functions) overR class="a-plus-plus"> n . In the case where, moreover,p(x) = (x class="a-plus-plus"> T Ax)class="a-plus-plus">1/2, withA being a symmetric positive definite matrix, a solution method is developed which is based on the red.c.ion of the problem to the global minimization of a concave function over a compact convex set.
暂无评论