Convex minimization problem

In this paper, we propose a generalized Nesterov algorithm for the constrained optimization problems on a closed convex set. We prove the convergence as well as the convergence rate of the proposed algorithm. First, we present a new algorithm based on the generalization of Nesterov’s algorithm.

5p vigojek 02-02-2024 1 0   Download

The problem of guaranteed cost control in this paper for a class of two-dimensional (2D) systems is described by the Roesser model with multiplicative stochastic noises. A convex optimization problem with linear matrix inequality constraints is formulated to show the guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain systems.

10p visharma 20-10-2023 5 2   Download

Lecture Convex optimization - Chapter: Interior-point methods. In this chapter we discuss interior-point methods for solving convex optimization problems that include inequality constraints. This chapter presents the following content: Inequality constrained minimization, logarithmic barrier function and central path, barrier method, feasibility and phase I methods, complexity analysis via self-concordance, generalized inequalities.

32p runthenight09 16-05-2023 4 3   Download

Lecture Convex optimization - Chapter: Equality constrained minimization. This chapter presents the following content: Equality constrained minimization, eliminating equality constraints, Newton’s method with equality constraints, infeasible start Newton method, implementation.

19p runthenight09 16-05-2023 6 3   Download

Lecture Convex optimization - Chapter: Unconstrained minimization. This chapter presents the following content: Terminology and assumptions, gradient descent method, steepest descent method, Newton’s method, self-concordant functions, implementation.

30p runthenight09 16-05-2023 4 3   Download

In this section, we recall some notations and properties of differentiable convex functions, differentiable functions that the gradient vectors are Lipschitz contiuous. These notations and properties are used in the proofs of main results in this paper.

4p vipatriciawoertz 30-05-2022 8 1   Download

In this paper, we propose a globally optimal scheduling scheme and a locally optimal scheduling scheme for EV charging and discharging. We first formulate a global scheduling optimization problem, in which the charging powers are optimized to minimize the total cost of all EVs which perform charging and discharging during the day. The globally optimal solution provides the globally minimal total cost.

3p vistephenhawking 26-04-2022 12 2   Download

In this paper we propose results on zero duality gap in vector optimization problems posed in a real locally convex Hausdorff topological vector space with a vector-valued objective function to be minimized under a set and a convex cone constraint. These results are then applied to linear programming.

14p nguaconbaynhay12 03-06-2021 13 1   Download

In this paper the duality and optimality of a class of constrained convex quadratic optimization problems have been studied. Furthermore, the global optimality condition of a class of interval quadratic minimization problems has also been discussed.

7p danhnguyentuongvi27 19-12-2018 19 1   Download

In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential. Suitable examples illustrating the non emptiness of the newly defined classes of functions and their relationships with classical notions of pseudoconvexity and quasiconvexity are provided.

16p danhnguyentuongvi27 19-12-2018 37 1   Download

Considering the problem of the minimal triangulation for a given polyhedra (dividing polyhedra into tetrahedra) it is known that the cone triangulation provides the number of tetrahedra which is the smallest, or the closest to it. It is also shown that when we want to know whether the cone triangulation is the minimal one, it is necessary to find the order of all vertices, as well as the order of “separating circles”.

14p vinguyentuongdanh 19-12-2018 13 0   Download

In this paper, we introduce a new implicit shrinking algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of relatively nonexpansive mappings in the framework of Banach spaces. Our results are refinement as well as generalization of several well-known results in the current literature. As a consequence, we give some applications for solving variational inequality problems and convex minimization problems in Banach spaces.

7p doctorstrange1 21-06-2018 34 1   Download

When training the parameters for a natural language system, one would prefer to minimize 1-best loss (error) on an evaluation set. Since the error surface for many natural language problems is piecewise constant and riddled with local minima, many systems instead optimize log-likelihood, which is conveniently differentiable and convex. We propose training instead to minimize the expected loss, or risk. We define this expectation using a probability distribution over hypotheses that we gradually sharpen (anneal) to focus on the 1-best hypothesis. ...

8p hongvang_1 16-04-2013 37 1   Download

Abstract. The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B is minimal. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this paper we propose and solve the following problem: on a given nonempty closed convex subset of Rs , find a point such that the sum of the distances from that point to n given nonempty closed convex subsets of...

96p camchuong_1 10-12-2012 52 4   Download

Iterative Recovery Algorithms 34.3 Spatially Invariant Degradation 34.4 Matrix-Vector Formulation Degradation Model • Basic Iterative Restoration Algorithm • Convergence • Reblurring Basic Iteration • Least-Squares Iteration 34.5 Matrix-Vector and Discrete Frequency Representations 34.6 Convergence Basic Iteration • Iteration with Reblurring 34.7 Use of Constraints The Method of Projecting Onto Convex Sets (POCS) 34.8 Class of Higher Order Iterative Algorithms 34.

20p longmontran 18-01-2010 85 7   Download