Optimization Letters最新文献

Current methodologies for finding portfolio rules under the Merton framework employ hard-to-implement numerical techniques. This work presents a methodology that can derive an allocation à la Merton in a spreadsheet, under an incomplete market with a time-varying dividend yield and long-only constraints. The first step of the method uses the martingale approach to obtain a portfolio rule in a complete artificial market. The second step derives a closed-form optimal solution satisfying the long-only constraints, from the unconstrained solution of the first step. This is done by determining closed-form Lagrangian dual processes satisfying the primal-dual optimality conditions between the true and artificial markets. The last step estimates the parameters defined in the artificial market, to then obtain analytical approximations for the hedging demand component within the optimal portfolio rule of the previous step. The methodology is tested with real market data from 16 US stocks from the Dow Jones. The results show that the proposed solution delivers higher financial wealth than the myopic solution, which does not consider the time-varying nature of the dividend yield. The sensitivity analysis carried out on the closed-form solution reveals that the difference with respect to the myopic solution increases when the price of the risky asset is more sensitive to the dividend yield, and when the dividend yield presents a higher probability of diverging from the current yield. The proposed solution also outperforms a known Merton-type solution that derives the Lagrangian dual processes in another way.

We consider the generalized Newton method (GNM) for the absolute value equation (AVE) (Ax-|x|=b). The method has finite termination property whenever it is convergent, no matter whether the AVE has a unique solution. We prove that GNM is convergent whenever (rho (|A^{-1}|)<1/3). We also present new results for the case where (A-I) is a nonsingular M-matrix or an irreducible singular M-matrix. When (A-I) is an irreducible singular M-matrix, the AVE may have infinitely many solutions. In this case, we show that GNM always terminates with a uniquely identifiable solution, as long as the initial guess has at least one nonpositive component.

We consider the problem of determining the optimal node interception strategy during influence propagation over a (directed) network (G=(V,A)). More specifically, this work aims to find an interception set (D subseteq V) such that the influence spread over the remaining network (G backslash D) under the linear threshold diffusion model is minimized. We prove its NP-hardness, even in the case when G is an undirected graph with unit edge weights. An exact algorithm based on integer linear programming and delayed constraint generation is proposed to determine the most critical nodes in the influence propagation process. Additionally, we investigate the technique of lifting inequalities of minimal activation sets. Experiments on the connected Watts-Strogatz small-world networks and real-world networks are also conducted to validate the effectiveness of our methodology.

In this article, we study weak stationarity conditions (A- and C-) for a particular class of degenerate stochastic mathematical programming problems with complementarity constraints (SMPCC, for short). Importance of the weak stationarity concepts in absence of SMPCC-LICQ are presented through toy problems in which the point of local or global minimizers are weak stationary points rather than satisfying other stronger stationarity conditions. Finally, a well known technique to solve stochastic programming problems, namely sample average approximation (SAA) method, is studied to show the significance of the weak stationarity conditions for degenerate SMPCC problems. Consistency of weak stationary estimators are established under weaker constraint qualifications than SMPCC-LICQ.

We propose a multistart algorithm to identify all local minima of a constrained, nonconvex stochastic optimization problem. The algorithm uniformly samples points in the domain and then starts a local stochastic optimization run from any point that is the “probabilistically best” point in its neighborhood. Under certain conditions, our algorithm is shown to asymptotically identify all local optima with high probability; this holds even though our algorithm is shown to almost surely start only finitely many local stochastic optimization runs. We demonstrate the performance of an implementation of our algorithm on nonconvex stochastic optimization problems, including identifying optimal variational parameters for the quantum approximate optimization algorithm.

In the game theoretical approach of the basic problem in Combinatorial Search an adversary thinks of a defective element d of an n-element pool X, and the questioner needs to find x by asking questions of type is (din Q?) for certain subsets Q of X. We study cooperative versions of this problem, where there are multiple questioners, but not all of them learn the answer to the queries. We consider various models that differ in how it is decided who gets to ask the next query, who obtains the answer to the query, and who needs to know the defective element by the end of the process.

We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our definition is less conservative than those found in the existing literature, and it can be viewed as an interpolation between fully exact and the existing inexact first-order oracle definitions. We analyze the convergence behavior of a (fast) inexact proximal gradient method using such an oracle for solving (non)convex composite minimization problems. We derive complexity estimates and study the dependence between the accuracy of the oracle and the desired accuracy of the gradient or of the objective function. Our results show that better rates can be obtained both theoretically and in numerical simulations when q is large.

This work addresses a parallel batch machine scheduling problem subject to tardiness penalties, release dates, and incompatible job families. In this environment, jobs of the same family are partitioned into batches and each batch is assigned to a machine. The objective is to determine the sequence in which the batches will be processed on each machine with a view of minimizing the total weighted tardiness. To solve the problem, we propose a population-based iterated local search algorithm that makes use of multiple neighborhood structures and an efficient perturbation mechanism. The algorithm also incorporates the time window decomposition (TWD) heuristic to generate the initial population and employs population control strategies aiming to promote individuals with higher fitness by combining the total weighted tardiness with the contribution to the diversity of the population. Extensive computational experiments were conducted on 4860 benchmark instances and the results obtained compare very favorably with those found by the best existing algorithms.

In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores and the minimization of the loss function in the training phase. In this paper, we provide a complete theoretical setting that formalizes weighted classification metrics and then allows the construction of losses that drive the model to optimize these metrics of interest. After a detailed theoretical analysis, we show that our framework includes as particular instances well-established approaches such as classical cost-sensitive learning, weighted cross entropy loss functions and value-weighted skill scores.

For given edge-capacitated connected graph and two its vertices s and t, the bottleneck (or (max min )) path problem is to find the maximum value of path-minimum edge capacities among all paths, connecting s and t. It can be generalized by finding the bottleneck values between s and all possible t. These problems arise as subproblems in the known maximum flow problem, having applications in many real-life tasks. For any graph with n vertices and m edges, they can be solved in O(m) and O(t(m, n)) times, respectively, where (t(m,n)=min (m+nlog (n),malpha (m,n))) and (alpha (cdot ,cdot )) is the inverse Ackermann function. In this paper, we generalize of the bottleneck path problems by considering their versions with k sources. For the first of them, where k pairs of sources and targets are (offline or online) given, we present an (O((m+k)log (n)))-time randomized and an (O(m+(n+k)log (n)))-time deterministic algorithms for the offline and online versions, respectively. For the second one, where the bottleneck values are found between k sources and all targets, we present an (O(t(m,n)+kn))-time offline/online algorithm.