MAP inference in continuous probabilistic models has largely been restricted to convex density functions in order to guarantee tractability of the underlying model, since high-dimensional nonconvex optimization problems contain a combinatorial number of local minima, making them extremely challenging for convex optimization techniques. This choice has resulted in significant computational advan...

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points that are obtained over time through costly observations. This paper presents an optimization framework that takes into account the information collection (ob...

A global optimization based approach for nding all homogeneous azeotropes in multicompo-nent mixtures is presented. The global optimization approach is based on a branch and bound framework in which upper and lower bounds on the solution are reened by successively partitioning the target region into small disjoint rectangles. The objective of such an approach is to locate all global minima sinc...

In this paper, by virtue of separation theorems convex sets and scalarization functions, some minimax inequalities are first considered. As applications, existence vector equilibrium problems with different order structures were also obtained.

In this paper we propose a mathematical programming model for a large drinking water supply network and discuss some possible extensions. The proposed optimization model is of a real water distribution network, the largest water supply network in Flanders. The problem is nonlinear, nonconvex and involves some binary variables, making it belong to the class of NP-hard problems. We discuss a way ...

Many tasks in imaging can be modeled via the minimization of a nonconvex composite function. A popular class of algorithms for solving such problems are majorizationminimization techniques which iteratively approximate the composite nonconvex function by a majorizing function that is easy to minimize. Most techniques, e.g. gradient descent, utilize convex majorizers in order guarantee that the ...

This paper concerns the problem of recovering an unknown but structured signal x ∈ Rn from m quadratic measurements of the form yr = ∣⟨ar,x⟩∣ for r = 1,2, . . . ,m. We focus on the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal (m << n). We formulate the recovery problem as a nonconvex optimization problem where prior structur...

In this paper, we study a solution approach for set optimization problems with respect to the lower less relation. This can serve as base numerically solving by using established solvers from multiobjective optimization. Our strategy consists of deriving parametric family whose optimal sets approximate, in specific sense, that set-valued problem arbitrary accuracy. We also examine particular cl...

It is well known that the stochastic optimization problem can be regarded as one of most hard problems since, in cases, values f and its gradient are often not easily to solved, or F(∙, ξ) normally given clearly (or) distribution function P equivocal. Then an effective algorithm successfully designed used solve this interesting work. This paper designs bigger subspace algorithms for solving non...