This paper proposes real-time sequential convex programming (RTSCP), a method for solving a sequence of nonlinear optimization problems depending on an online parameter. We provide a contraction estimate for the proposed method and, as a byproduct, a new proof of the local convergence of sequential convex programming. The approach is illustrated by an example where RTSCP is applied to nonlinear...

We define and analyze two kinds of stability in E-convex programming problem in which the feasible domain is affected by an operator E. The first kind of this stability is that the set of all operators E that make an optimal set stable while the other kind is that the set of all operators E that make certain side of the feasible domain still active. 2000 Mathematics Subject Classification. 90Cxx.

In the paper, we focus primarily on the problem of recovering a linear form g x of unknown “signal” x known to belong to a given convex compact set X ⊂ R from N independent realizations of a random variable ι taking values in a finite set, the distribution p of ι being affinely parameterized by x: p = Ax + b. With no additional assumptions on X and A, we develop minimax optimal, within an absol...

It has long been known that a wide class of problems in optimal control can be stated as infinite-dimensional convex optimization problems, where the Bellman equation is relaxed to inequality. In this paper we continue our recent efforts to show how this formulation can be used for numerical computation of optimal cost functions and control laws. In particular, we discuss new forms of discretiz...

The paper deals with convex parametric programming problems. In this paper convex parametric programming transform to a neural network model and then we solve neural network model with one of numerical methods. Finally, simple numerical examples are provided for the sake of illustration. 2006 Elsevier Inc. All rights reserved.

We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization. In the main part of the paper we show that if U i...

A convex body K in R has associated with it a unique circumscribed ellipsoid CE(K) with minimum volume, and a unique inscribed ellipsoid IE(K) with maximum volume. We first give a unified, modern exposition of the basic theory of these extremal ellipsoids using the semi–infinite programming approach pioneered by Fritz John in his seminal 1948 paper. We then investigate the automorphism groups o...

A large class of separable quadratic programming problems is presented The problems in the class can be solved in linear time The class in cludes the separable convex quadratic transportation problem with a xed number of sources and separable convex quadratic programming with nonnegativity con straints and a xed number of linear equality constraints

In recent years, there has been an increasing interest in studying the develpoment of optimality conditions for nondifferentiable multiobjective programming problems. Many authors established and employed some different Kuhn and Tucker type necessary conditions or other type necessary conditions to research optimal solutions; see [1–27] and references therein. In [7], Lai and Ho used the Pareto...