A complete characterization of disjunctive conic cuts for mixed integer second order cone optimization

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique, we show that one can extend our previous results to the case in which that intersection is unbounded. We provide a complete characterization in closed form of the conic inequalities required to describe the convex hull when the hyperplanes defining the disjunction are parallel.     

Proximal-gradient algorithms for fractional programming

In this paper, we propose two proximal-gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with respect to the nonsmooth numerator and a gradient step with respect to the smooth denominator. The algorithm in case of a concave denominator has the particularity that it generates sequences which approach both the (global) optimal solutions set and the optimal objective value of the underlying fractional programming problem. In case of a convex denominator the numerical scheme approaches the set of critical points of the objective function, provided the latter satisfies the Kurdyka-?ojasiewicz property.     

Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval-objective function are convex.     

Generalized asymptotic functions in nonconvex multiobjective optimization problems

In this paper, we use generalized asymptotic functions and second-order asymptotic cones to develop a general existence result for the nonemptiness of the proper efficient solution set and a sufficient condition for the domination property in nonconvex multiobjective optimization problems. A new necessary condition for a point to be efficient or weakly efficient solution is given without any convexity assumption. We also provide a finer outer estimate for the asymptotic cone of the weakly efficient solution set in the quasiconvex case. Finally, we apply our results to the linear fractional multiobjective optimization problem.     

A stochastic portfolio optimization model with complete memory

In this article, we consider a portfolio optimization problem of the Merton’s type with complete memory over a finite time horizon. The problem is formulated as a stochastic control problem on a finite time horizon and the state evolves according to a process governed by a stochastic process with memory. The goal is to choose investment and consumption controls such that the total expected discounted utility is maximized. Under certain conditions, we derive the explicit solutions for the associated Hamilton–Jacobi–Bellman (HJB) equations in a finite-dimensional space for exponential, logarithmic, and power utility functions. For those utility functions, verification results are established to ensure that the solutions are equal to the value functions, and the optimal controls are also derived.     

OBJECT-ORIENTED FINITE ELEMENT ANALYSIS AND PROGRAMMING IN VC++

ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｎｃｅｆｉｎｉｔｅｅｌｅｍｅｎｔａｎａｌｙｓｉｓｐｒｏｇｒａｍｓｄｅａｌｗｉｔｈｔｈｅｔｈｅｏｒｉｅｓａｎｄｍｅｔｈｏｄｓｏｆｔｈｒｅｅｆｉｅｌｄｓｏｆｍｅｃｈａｎｉｃｓ,ａｐｐｌｉｅｄｍａｔｈｅｍａｔｉｃｓａｎｄｃｏｍｐｕｔｅｒｓｃｉｅｎｃｅ,ｔｈｅｙａｒｅｃｏｍｐｌｉｃａｔｅｄａｎｄｅｒｒｏｒ＿ｐｒｏｎｅ .Ｄｕｒｉｎｇｄｅｖｅｌｏｐｍｅｎｔｐｅｏｐｌｅａｌｌｔｈｒｏｕｇｈｓｅｅｋｔｈｅｍｅｔｈｏｄｔｏｉｍｐｒｏｖｅｐｒｏｇｒａｍｓ.Ｔｈｅｏｂｊｅｃｔ＿ｏｒｉｅｎｔｅ…     

An efficient method for structural optimization

Based on the dual theory of nonlinear mathematical programming and the second order Taylor series expansions of functions, an efficient algorithm for structural optimum design has been developed. The main advantages of this method are the generality in use, the efficiency in computation and the capability in identifying automatically the set of active constraints. On the basis of the virtual work principle, formulas in terms of element stresses for the first and second order derivatives of nodal displacement and stress with respect to design variables are derived. By applying the Saint-Venant's principle, the computational efforts involved in the Hessian matrix associated with the iterative expression can be significantly reduced. This method is especially suitable for optimum design of large scale structures. Several typical examples have been optimized to test its uasefulness.     

UNILATERAL CONTACT PROBLEMS USING QUASI-ACTIVE SET STRATEGY

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅａｒｅｏｆｔｅｎｓｏｍｅｓｔｒｕｃｔｕｒｅｓｏｒｃｏｍｐｏｎｅｎｔｓｗｈｉｃｈｃａｎｏｎｌｙｔｒａｎｓｆｅｒｏｎｅｓｐｅｃｉａｌｆｏｒｍｏｆｓｔｒｅｓｓ,ｓｕｃｈａｓｔｈｅｃａｂｌｅｗｈｉｃｈｃａｎｏｎｌｙｂｅｕｓｅｄｔｏｔｒａｎｓｆｅｒｔｈｅｔｅｎｓｉｏｎｓｔｒｅｓｓａｎｄｔｈｅｃｏｎｔａｃｔｃｏｍｐｏｎｅｎｔｗｈｉｃｈｃａｎｏｎｌｙｔｒａｎｓｆｅｒｔｈｅｐｒｅｓｓｕｒｅ.Ｉｎｇｅｎｅｒａｌ,ｓｕｃｈｐｒｏｂｌｅｍｓａｒｅｏｆｔｅｎｃａｌｌｅｄｔｈｅｕｎｉｌａｔ…