In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

In this paper, a new pair of Mond-Weir type multiobjective second-order symmetric dual models with cone constraints is formulated in which the objective function is optimised with respect to an arbitrary closed convex cone. Usual duality relations are further established under K-η-bonvexity/second-order symmetric dual K-H-convexity assumptions. A nontrivial example has also been illustrated to ...

Historically, much of the theory and practice in nonlinear optimization has revolved around the quadratic models. Though quadratic functions are nonlinear polynomials, they are well structured and easy to deal with. Limitations of the quadratics, however, become increasingly binding as higher degree nonlinearity is imperative in modern applications of optimization. In the recent years, one obse...

In this paper, we present a novel and computationally efficient approach to constrained discrete-time dynamic asset allocation over multiple periods. This technique is able to control portfolio expectation and variance at both final and intermediate stages of the decision horizon and may account for proportional transaction costs and intertemporal dependence of the return process. A key feature...

NIE, TIANTIAN. Quadratic Programming with Discrete Variables. (Under the direction of Dr. Shu-Cherng Fang.) In this dissertation, we study the quadratic programming problem with discrete variables (DQP). DQP is important in theory and practice, but the combination of the quadratic feature of the objective function and the discrete nature of the feasible domain makes it hard to solve. In this th...

Large convex quadratic programs, where constraints are of box type only, can be solved quite eeciently 1], 2], 12], 13], 16]. In this paper an exact quadratic augmented Lagrangian with bound constraints is constructed which allows one to use these methods for general constrained convex quadratic programming. This is in contrast to well known exact diierentiable penalty functions for this type o...

We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprar...

The following question arises in stochastic programming: how can one approximate a noisy convex function with a convex quadratic function that is optimal in some sense. Using several approaches for constructing convex approximations we present some optimization models yielding convex quadratic regressions that are optimal approximations in L1, L∞ and L2 norm. Extensive numerical experiments to ...

The Helton-Nie Conjecture (HNC) is the proposition that every convex semialgebraic set is a spectrahedral shadow. Here we prove that HNC is equivalent to another proposition related to quadratically constrained quadratic programming. Namely, that the convex hull of the rank-one elements of any spectrahedron is a spectrahedral shadow. In the case of compact convex semialgebraic sets, the spectra...