Global optimality conditions for some classes of polynomial integer programming problems

In this paper, some verifiable necessary global optimality conditions and sufficient global optimality conditions for some classes of polynomial integer programming problems are established. The relationships between these necessary global optimality conditions and these sufficient global optimality conditions are also discussed. The main theoretical tool for establishing these optimality conditions is abstract convexity

Global optimality conditions for mixed integer weakly concave programming problems

In this paper, some necessary and some suffcient global optimality conditions for a class of mixed integer programming problems whose objective functions are the difference of quadratic functions and convex functions are established. The numerical examples are also presented to show the significance of the global optimality conditions for this class of programming problems. Copyright © 2010 Watam Press

Global optimality conditions and optimization methods for constrained polynomial programming problems

The general constrained polynomial programming problem (GPP) is considered in this paper. Problem (GPP) has a broad range of applications and is proved to be NP-hard. Necessary global optimality conditions for problem (GPP) are established. Then, a new local optimization method for this problem is proposed by exploiting these necessary global optimality conditions. A global optimization method is proposed for this problem by combining this local optimization method together with an auxiliary function. Some numerical examples are also given to illustrate that these approaches are very efficient. (C) 2015 Elsevier Inc. All rights reserved

Sufficient conditions for global optimality of semidefinite optimization

In this article, by using the Lagrangian function, we investigate the sufficient global optimality conditions for a class of semi-definite optimization problems, where the objective function are general nonlinear, the variables are mixed integers subject to linear matrix inequalities (LMIs) constraints as well as bounded constraints. In addition, the sufficient global optimality conditions for general nonlinear programming problems are derived, where the variables satisfy LMIs constraints and box constraints or bivalent constraints. Furthermore, we give the sufficient global optimality conditions for standard semi-definite programming problem, where the objective function is linear, the variables satisfy linear inequalities constraints and box constraints. © 2012 Quan et al

Global optimality conditions and optimization methods for quadratic assignment problems

In this paper some global optimality conditions for general quadratic {0, 1} programming problems with linear equality constraints are discussed and then some global optimality conditions for quadratic assignment problems (QAP) are presented. A local optimization method for (QAP) is derived according to the necessary global optimality conditions. A global optimization method for (QAP) is presented by combining the sufficient global optimality conditions, the local optimization method and some auxiliary functions. Some numerical examples are given to illustrate the efficiency of the given optimization methods. © 2011 Elsevier Inc. All rights reserved

Upwelling velocity and ventilation in the western South China Sea deduced from CFC-12 and SF6 observations

This study presents observations of the transient tracers CFC-12 and SF6 in the western South China Sea during the fall of 2015. A CFC-12 maximum was discovered in the western South China Sea at the subsurface layer (150–200 m), which could be traced back to the North Pacific Tropical Water. The transit time distribution approach was used to estimate the ventilation time in this area. The constrained Δ /Γ ratio of 0.5 was obtained using CFC-12/SF6 tracer pair. This ratio is lower than the empirical unit ratio of one as used for previous estimates. Waters in the northern region of the western South China Sea appear younger than waters in the southern region. The water mass corresponding to the salinity minimum has a mean age of ∼67 ± 16 years along the 15º N line (marked by the red dashed rectangle in Fig. 1), which increases to ∼76 ± 18 years along the 10º N line (blue dashed rectangle, Fig. 1). The higher mean ages indicate that the intermediate water was ventilated from the North Pacific, which is far distant from the South China Sea. The column inventory of Cant is ∼31.3 mol C m–2. Upwelling velocities of up to ∼55 × 10–5 m s–1 was computed using the tracer data, indicating that tracer-free water as yet not influenced by human perturbation could be carried to the upper layer by upwelling. Using the transit time distribution derived mean age with transient tracers provides a possible way to determine the ventilation time scale for the study area

Pd-Pt random alloy nanocubes with tunable compositions and their enhanced electrocatalytic activities

Monodisperse, highly-selective sub-10 nm Pd-Pt random alloy nanocubes have been successfully synthesized in aqueous solution, and the electrocatalytic activity of these Pd-Pt alloys towards formic acid oxidation was investigated and compared with the activity of Pd sub-10 nm nanocubes, and the commercial Pd and Pt black.NSFC [20725102, 20921001]; Fok Ying Tung Education Foundation [111012]; State Key Project of Fundamental Research for Nanoscience and Nanotechnology [2006CB932301

Optimality conditions and optimization methods for quartic polynomial optimization

In this paper multivariate quartic polynomial optimization program (QPOP) is considered. Quartic optimization problems arise in various practical applications and are proved to be NP hard. We discuss necessary global optimality conditions for quartic problem (QPOP). And then we present a new (strongly or ε-strongly) local optimization method according to necessary global optimality conditions, which may escape and improve some KKT points. Finally we design a global optimization method for problem (QPOP) by combining the new (strongly or ε-strongly) local optimization method and an auxiliary function. Numerical examples show that our algorithms are efficient and stable

Optimization methods for box-constrained nonlinear programming problems based on linear transformation and Lagrange interpolating polynomials

In this paper, an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials. Based on this condition, two new local optimization methods are developed. The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker (KKT) points in general. Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method. Some numerical examples are reported to show the effectiveness of the proposed methods. © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg

Global optimality conditions and optimization methods for polynomial programming problems

This paper is concerned with the general polynomial programming problem with box constraints, including global optimality conditions and optimization methods. First, a necessary global optimality condition for a general polynomial programming problem with box constraints is given. Then we design a local optimization method by using the necessary global optimality condition to obtain some strongly or -strongly local minimizers which substantially improve some KKT points. Finally, a global optimization method, by combining the new local optimization method and an auxiliary function, is designed. Numerical examples show that our methods are efficient and stable